## Universal families and hypercyclic operators.(English)Zbl 0933.47003

From the author’s introduction: Analysis is the study of limiting processes. Not every limiting process, of course, converges, but examples have been found where processes diverge in a maximal way. Such an extreme behaviour is often linked with the phenomenon of universality, which constitutes the topic of this survey.
From an abstract point of view, the phenomenon of universality may be described as follows. We have a topological space $$X$$ of objects, a topological space $$Y$$ of elements to be approximated and a family (usually a sequence) $$T_\iota: X\to Y$$ $$(\iota\in I)$$ of mappins. Then an object $$x$$ in $$X$$ is called universal if every element $$y$$ in $$Y$$ can be approximated by certain $$T_\iota x$$, that is, if the set $$\{T_\iota x:\iota\in I\}$$ is dense in $$Y$$.
Introduction.
Part I. General Theory.
1. Universal families. 1a. The Universality Criterion; 1b. The set of universal elements; 1c. Universality in linear spaces; 1d. Universal series.
2. Hypercyclic operators. 2a. The Hypercyclicity criterion; 2b. The set of hypercyclic vectors; 2c. Derived hypercyclicity; 2d. Existence of hypercyclic operators.
Part II. Specific Universal Families and Hypercyclic Operators.
3. The real analysis setting. 3a. Universal power and Taylor series; 3b. Universal primitives; 3c. Universal orthogonal series; 3d. Universal series for convergence a.e.; 3e. Further real universalities and hypercyclicities.
4. The complex analysis setting. 4a. Universal and hypercyclic composition operators; 4. Holomorphic monsters; 4c. Hypercyclic differential operators; 4d. Universal power and Taylor series; 4e. Universal matrices.
5. Hypercyclic operators in classical Banach spaces.
6. A concrete universal object: the Riemann zeta-function.
References; Bibliography.

### MSC:

 47A16 Cyclic vectors, hypercyclic and chaotic operators 47A65 Structure theory of linear operators 54H99 Connections of general topology with other structures, applications 47A35 Ergodic theory of linear operators 47-02 Research exposition (monographs, survey articles) pertaining to operator theory 54-02 Research exposition (monographs, survey articles) pertaining to general topology
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### References:

 [1] Yukitaka Abe, Universal holomorphic functions in several variables, Analysis 17 (1997), no. 1, 71 – 77. · Zbl 0878.32002 · doi:10.1524/anly.1997.17.1.71 [2] Y. Abe, Universal functions on complex special linear groups, (Proc. Conf., Poznań, 1998) (to appear). 4a [3] Y. Abe and P. Zappa, Universal functions on complex general linear groups, J. Approx. Theory (to appear). 4a · Zbl 0955.30038 [4] M. P. Aldred and D. H. Armitage, Harmonic analogues of G. R. MacLane’s universal functions, J. London Math. Soc. (2) 57 (1998), no. 1, 148 – 156. · Zbl 0922.31004 · doi:10.1112/S0024610798005699 [5] M. P. Aldred and D. H. Armitage, Harmonic analogues of G. R. Mac Lane’s universal functions. II, J. Math. Anal. Appl. 220 (1998), no. 1, 382 – 395. · Zbl 0945.31001 · doi:10.1006/jmaa.1997.5892 [6] G. Alexits, Konvergenzprobleme der Orthogonalreihen, Verlag der Ungarischen Akademie der Wissenschaften, Budapest, 1960 (German). · Zbl 0097.27702 [7] Shamim I. Ansari, Hypercyclic and cyclic vectors, J. Funct. Anal. 128 (1995), no. 2, 374 – 383. · Zbl 0853.47013 · doi:10.1006/jfan.1995.1036 [8] Shamim I. Ansari, Existence of hypercyclic operators on topological vector spaces, J. Funct. Anal. 148 (1997), no. 2, 384 – 390. , https://doi.org/10.1006/jfan.1996.3093 Fernando León-Saavedra and Alfonso Montes-Rodríguez, Linear structure of hypercyclic vectors, J. Funct. Anal. 148 (1997), no. 2, 524 – 545. · Zbl 0999.47009 · doi:10.1006/jfan.1996.3084 [9] D. H. Armitage, Dense vector spaces of universal harmonic functions, Advances in multivariate approximation (Proc. Conf., Witten-Bommerholz, 1998) (to appear). 3e,4c [10] D. H. Armitage and P. M. Gauthier, Recent developments in harmonic approximation, with applications, Results Math. 29 (1996), no. 1-2, 1 – 15. · Zbl 0859.31001 · doi:10.1007/BF03322201 [11] R. Aron and J. Bès, Hypercyclic differentiation operators, Function Spaces (Proc. Conf., Edwardsville, IL, 1998), 39-46, Amer. Math. Soc., Providence, RI, 1999. 4a,4c [12] Vincenzo Aversa and Rosalba Carrese, A universal primitive for functions of many variables, Rend. Circ. Mat. Palermo (2) 32 (1983), no. 1, 131 – 138 (Italian, with English summary). · Zbl 0536.28003 · doi:10.1007/BF02851109 [13] B. Bagchi, The statistical behaviour and universality properties of the Riemann zeta function and other allied Dirichlet series, Thesis, Indian Statistical Institute, Calcutta, 1981. 6 [14] Bhaskar Bagchi, A joint universality theorem for Dirichlet \?-functions, Math. Z. 181 (1982), no. 3, 319 – 334. · Zbl 0479.10028 · doi:10.1007/BF01161980 [15] A. V. Bakhshetsyan and V. G. Krotov, On universal series in Schauder systems, Izv. Akad. Nauk Armyan. SSR Ser. Mat. 16 (1981), no. 1, 44 – 53, 82 (Russian, with English and Armenian summaries). · Zbl 0516.42034 [16] Тригонометрические ряды, Щитх тхе едиториал цоллаборатион оф П. Л. Ул$$^{\приме}$$јанов, Государств. Издат. Физ.-Мат. Лит., Мосцощ, 1961 (Руссиан). [17] Bernard Beauzamy, Un opérateur, sur l’espace de Hilbert, dont tous les polynômes sont hypercycliques, C. R. Acad. Sci. Paris Sér. I Math. 303 (1986), no. 18, 923 – 925 (French, with English summary). · Zbl 0612.47003 [18] Bernard Beauzamy, An operator on a separable Hilbert space with many hypercyclic vectors, Studia Math. 87 (1987), no. 1, 71 – 78. · Zbl 0647.46024 [19] Bernard Beauzamy, Opérateurs de rayon spectral strictement supérieur à 1, C. R. Acad. Sci. Paris Sér. I Math. 304 (1987), no. 10, 263 – 266 (French, with English summary). · Zbl 0606.47003 [20] Bernard Beauzamy, Introduction to operator theory and invariant subspaces, North-Holland Mathematical Library, vol. 42, North-Holland Publishing Co., Amsterdam, 1988. · Zbl 0663.47002 [21] Bernard Beauzamy, An operator on a separable Hilbert space with all polynomials hypercyclic, Studia Math. 96 (1990), no. 1, 81 – 90. · Zbl 0724.47001 [22] Luis Bernal González, Derivative and antiderivative operators and the size of complex domains, Ann. Polon. Math. 59 (1994), no. 3, 267 – 274. · Zbl 0843.47019 [23] Luis Bernal-González, Universal functions for Taylor shifts, Complex Variables Theory Appl. 31 (1996), no. 2, 121 – 129. · Zbl 0865.47024 [24] Luis Bernal-González, On universal entire functions with zero-free derivatives, Arch. Math. (Basel) 68 (1997), no. 2, 145 – 150. · Zbl 0865.30041 · doi:10.1007/s000130050043 [25] Luis Bernal-González, On hypercyclic operators on Banach spaces, Proc. Amer. Math. Soc. 127 (1999), no. 4, 1003 – 1010. · Zbl 0911.47020 [26] L. Bernal-González, Hypercyclic sequences of differential and antidifferential operators, J. Approx. Theory 96 (1999), 323-337. CMP 99:08 1c,2a,4c · Zbl 0957.47009 [27] L. Bernal-González, Densely hereditarily hypercyclic sequences and large hypercyclic mainfolds, Proc. Amer. Math. Soc. (to appear). CMP 99:02 1a,1b,1c,2a,2c,4c [28] L. Bernal-González and M. C. Calderón-Moreno, A Seidel-Walsh theorem with linear differential operators, Arch. Math. (to appear). 4a · Zbl 1025.30031 [29] Luis Bernal González and Alfonso Montes-Rodríguez, Universal functions for composition operators, Complex Variables Theory Appl. 27 (1995), no. 1, 47 – 56. · Zbl 0838.30032 [30] Luis Bernal González and Alfonso Montes Rodríguez, Non-finite-dimensional closed vector spaces of universal functions for composition operators, J. Approx. Theory 82 (1995), no. 3, 375 – 391. · Zbl 0831.30024 · doi:10.1006/jath.1995.1086 [31] N. C. Bernardes, On orbits of polynomial maps in Banach spaces, Quaestiones Math. (to appear). 2d · Zbl 0946.47042 [32] J. P. Bès, Invariant manifolds of hypercyclic vectors for the real scalar case, Proc. Amer. Math. Soc. 127 (1999), 1801-1804. CMP 99:10 2b,2d [33] J. Bès and A. Peris, Hereditarily hypercyclic operators, J. Funct. Anal. (to appear). 1b,2a,2c,2d,4c,5 · Zbl 0941.47002 [34] G. D. Birkhoff, Démonstration d’un théorème élémentaire sur les fonctions entières, C. R. Acad. Sci. Paris 189 (1929), 473-475. JFM 55:192 1a,2a,4a [35] Charles Blair and Lee A. Rubel, A universal entire function, Amer. Math. Monthly 90 (1983), no. 5, 331 – 332. · Zbl 0534.30029 · doi:10.2307/2975786 [36] Charles Blair and Lee Rubel, A triply universal entire function, Enseign. Math. (2) 30 (1984), no. 3-4, 269 – 274. · Zbl 0559.30033 [37] Antal Bogmér, On universal elements of series of linear operators, Mat. Lapok 31 (1978/83), no. 1-3, 195 – 196 (Hungarian). · Zbl 0557.40006 [38] A. Bogmér and A. Sövegjártó, On universal functions, Acta Math. Hungar. 49 (1987), no. 1-2, 237 – 239. · Zbl 0618.26003 · doi:10.1007/BF01956327 [39] J. Bonet, Hypercyclic and chaotic convolution operators, J. London Math. Soc. (to appear). 2c,2d,3e,4c · Zbl 0956.46029 [40] J. Bonet and A. Peris, Hypercyclic operators on non-normable Fréchet spaces, J. Funct. Anal. 159 (1998), 587-595. CMP 99:04 2d · Zbl 0926.47011 [41] Paul S. Bourdon, Invariant manifolds of hypercyclic vectors, Proc. Amer. Math. Soc. 118 (1993), no. 3, 845 – 847. · Zbl 0809.47005 [42] Paul S. Bourdon, The second iterate of a map with dense orbit, Proc. Amer. Math. Soc. 124 (1996), no. 5, 1577 – 1581. · Zbl 0853.54036 [43] Paul S. Bourdon and Joel H. Shapiro, Cyclic composition operators on \?², Operator theory: operator algebras and applications, Part 2 (Durham, NH, 1988) Proc. Sympos. Pure Math., vol. 51, Amer. Math. Soc., Providence, RI, 1990, pp. 43 – 53. [44] Paul S. Bourdon and Joel H. Shapiro, Cyclic phenomena for composition operators, Mem. Amer. Math. Soc. 125 (1997), no. 596, x+105. · Zbl 0996.47032 · doi:10.1090/memo/0596 [45] Andrew M. Bruckner, Differentiation of real functions, Lecture Notes in Mathematics, vol. 659, Springer, Berlin, 1978. · Zbl 0382.26002 [46] Z. Buczolich, On universal functions and series, Acta Math. Hungar. 49 (1987), no. 3-4, 403 – 414. · Zbl 0629.40001 · doi:10.1007/BF01951004 [47] X. H. Cao and Y. G. Wang, Hypercyclic and supercyclic operators (Chinese), Qufu Shifan Daxue Xuebao Ziran Kexue Ban 24 (1998), no. 4, 4-7. CMP 99:08 2d [48] F. S. Cater, Some higher-dimensional Marcinkiewicz theorems, Real Anal. Exchange 15 (1989/90), no. 1, 269 – 274. · Zbl 0704.26019 [49] K. C. Chan, Hypercyclicity of the operator algebra for a separable Hilbert space, J. Operator Theory 42 (1999), 231-244. 2b,5 [50] K. C. Chan, The density of hypercyclic operators on a Hilbert space, preprint. 2d · Zbl 1042.47007 [51] Kit C. Chan and Joel H. Shapiro, The cyclic behavior of translation operators on Hilbert spaces of entire functions, Indiana Univ. Math. J. 40 (1991), no. 4, 1421 – 1449. · Zbl 0771.47015 · doi:10.1512/iumj.1991.40.40064 [52] N. S. Čaščina, On the theory of a universal Dirichlet series, Izv. Vysš. Učebn. Zaved. Matematika 1963 (1963), no. 4 (35), 165 – 167 (Russian). [53] P. S. Chee, Universal functions in several complex variables, J. Austral. Math. Soc. Ser. A 28 (1979), no. 2, 189 – 196. · Zbl 0423.32002 [54] G. A. Čhaidze, Universal series, Sakharth. SSR Mecn. Akad. Moambe 86 (1977), no. 1, 45 – 47 (Russian, with Georgian and English summaries). [55] Charles K. Chui and Milton N. Parnes, Approximation by overconvergence of a power series, J. Math. Anal. Appl. 36 (1971), 693 – 696. · Zbl 0224.30006 · doi:10.1016/0022-247X(71)90049-7 [56] Wolfgang Desch, Wilhelm Schappacher, and Glenn F. Webb, Hypercyclic and chaotic semigroups of linear operators, Ergodic Theory Dynam. Systems 17 (1997), no. 4, 793 – 819. · Zbl 0910.47033 · doi:10.1017/S0143385797084976 [57] L. K. Dodunova, On the overconvergence of universal series, Izv. Vyssh. Uchebn. Zaved. Mat. 2 (1988), 19 – 22, 83 (Russian); English transl., Soviet Math. (Iz. VUZ) 32 (1988), no. 2, 27 – 30. [58] L. K. Dodunova, A generalization of the universality property of Faber polynomial series, Izv. Vyssh. Uchebn. Zaved. Mat. 12 (1990), 31 – 34 (Russian); English transl., Soviet Math. (Iz. VUZ) 34 (1990), no. 12, 37 – 40. · Zbl 0737.30002 [59] L. K. Dodunova, Approximation of analytic functions by de la Vallée-Poussin sums, Izv. Vyssh. Uchebn. Zaved. Mat. 3 (1997), 34 – 37 (Russian); English transl., Russian Math. (Iz. VUZ) 41 (1997), no. 3, 33 – 36. · Zbl 0908.30040 [60] S. M. Duĭos Ruis, On the existence of universal functions, Dokl. Akad. Nauk SSSR 268 (1983), no. 1, 18 – 22 (Russian). [61] S. M. Duĭos Ruis, Universal functions and the structure of the space of entire functions, Dokl. Akad. Nauk SSSR 279 (1984), no. 4, 792 – 795 (Russian). [62] Janet Dyson, Rosanna Villella-Bressan, and Glenn Webb, Hypercyclicity of solutions of a transport equation with delays, Nonlinear Anal. 29 (1997), no. 12, 1343 – 1351. · Zbl 0899.34046 · doi:10.1016/S0362-546X(96)00192-7 [63] O. P. Dzagnidze, On universal double series, Soobšč. Akad. Nauk Gruzin. SSR 34 (1964), 525 – 528 (Russian, with Georgian summary). [64] O. P. Dzagnidze, The universal harmonic function in the space \?_{\?}, Sakharth. SSR Mecn. Akad. Moambe 55 (1969), 41 – 44 (Russian, with Georgian and English summaries). [65] J. J. Edge, Universal trigonometric series, J. Math. Anal. Appl. 29 (1970), 507 – 511. · Zbl 0167.33701 · doi:10.1016/0022-247X(70)90064-8 [66] Hassan Emamirad, Hypercyclicité du semi-groupe de transport et le théorème de représentation de Lax et Phillips, C. R. Acad. Sci. Paris Sér. I Math. 325 (1997), no. 2, 157 – 162 (French, with English and French summaries). · Zbl 0880.35090 · doi:10.1016/S0764-4442(97)84591-0 [67] H. Emamirad, Hypercyclicity in the scattering theory for linear transport equation, Trans. Amer. Math. Soc. 350 (1998), no. 9, 3707 – 3716. · Zbl 0899.35071 [68] K. M. Èminyan, \?-universality of the Dirichlet \?-function, Mat. Zametki 47 (1990), no. 6, 132 – 137 (Russian); English transl., Math. Notes 47 (1990), no. 5-6, 618 – 622. · Zbl 0713.11058 · doi:10.1007/BF01170896 [69] Karin Faulstich, Summierbarkeit von Potenzreihen durch Riesz-Verfahren mit komplexen Erzeugendenfolgen, Mitt. Math. Sem. Giessen 139 (1979), iii+117 (German). · Zbl 0418.40008 [70] Karin Faulstich, Wolfgang Luh, and Ludwig Tomm, Universelle Approximation durch Riesz-Transformierte der geometrischen Reihe, Manuscripta Math. 36 (1981/82), no. 3, 309 – 321 (German, with English summary). · Zbl 0479.30023 · doi:10.1007/BF01322495 [71] E. Flytzanis, Unimodular eigenvalues and linear chaos in Hilbert spaces, Geom. Funct. Anal. 5 (1995), no. 1, 1 – 13. · Zbl 0827.46043 · doi:10.1007/BF01928214 [72] Xiao-Xiong Gan and Karl R. Stromberg, On universal primitive functions, Proc. Amer. Math. Soc. 121 (1994), no. 1, 151 – 161. · Zbl 0845.26005 [73] R. Garunkštis, The universality theorem with weight for the Lerch zeta-function, New Trends in Probability and Statistics, Vol. 4 (Proc. Conf., Palanga, 1996), 59-67, VSP, Utrecht; TEV, Vilnius, 1997. CMP 99:03 6 [74] Paul M. Gauthier, Uniform approximation, Complex potential theory (Montreal, PQ, 1993) NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 439, Kluwer Acad. Publ., Dordrecht, 1994, pp. 235 – 271. · Zbl 0810.30001 [75] V. I. Gavrilov and A. N. Kanatnikov, An example of a universal holomorphic function, Dokl. Akad. Nauk SSSR 265 (1982), no. 2, 274 – 276 (Russian). · Zbl 0514.30007 [76] W. Gehlen, W. Luh, and J. Müller, On the existence of O-universal functions, Complex Variables Theory Appl. (to appear). 4d · Zbl 1020.30004 [77] Bernard R. Gelbaum and John M. H. Olmsted, Counterexamples in analysis, The Mathesis Series, Holden-Day, Inc., San Francisco, Calif.-London-Amsterdam, 1964. · Zbl 1085.26002 [78] Robert M. Gethner and Joel H. Shapiro, Universal vectors for operators on spaces of holomorphic functions, Proc. Amer. Math. Soc. 100 (1987), no. 2, 281 – 288. · Zbl 0618.30031 [79] Gilles Godefroy, Opérateurs ayant un sous-espace dense de vecteurs hypercycliques, Séminaire d’Initiation à l’Analyse, Publ. Math. Univ. Pierre et Marie Curie, vol. 94, Univ. Paris VI, Paris, 1989, pp. Exp. No. 3, 6 (French). · Zbl 0719.47018 [80] Gilles Godefroy and Joel H. Shapiro, Operators with dense, invariant, cyclic vector manifolds, J. Funct. Anal. 98 (1991), no. 2, 229 – 269. · Zbl 0732.47016 · doi:10.1016/0022-1236(91)90078-J [81] Casper Goffman and George Pedrick, First course in functional analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1965. · Zbl 0122.11206 [82] Casper Goffman and Daniel Waterman, Basic sequences in the space of measurable functions, Proc. Amer. Math. Soc. 11 (1960), 211 – 213. · Zbl 0092.11701 [83] Casper Goffman and Daniel Waterman, A remark concerning universal series, J. Math. Anal. Appl. 40 (1972), 735 – 737. · Zbl 0271.28004 · doi:10.1016/0022-247X(72)90016-9 [84] S. M. Gonek, Analytic properties of zeta and L-functions, Thesis, Univ. of Michigan, Ann Arbor, 1979. 6 [85] M. González-Ortiz, F. León-Saavedra, and A. Montes-Rodríguez, Semi-Fredholm theory: hypercyclic and supercyclic subspaces, preprint. 2b,2c,2d · Zbl 1028.47007 [86] A. Good, On the distribution of the values of Riemann’s zeta function, Acta Arith. 38 (1980/81), no. 4, 347 – 388. · Zbl 0372.10029 [87] Eulalia Grande, Sur un théorème de Marcinkiewicz, Problemy Mat. 4 (1984), 35 – 41 (French, with Polish summary). · Zbl 0569.26006 [88] Karl-Goswin Große-Erdmann, Holomorphe Monster und universelle Funktionen, Mitt. Math. Sem. Giessen 176 (1987), iv+84 (German). Dissertation, University of Trier, Trier, 1987. [89] Karl-Goswin Grosse-Erdmann, On the universal functions of G. R. MacLane, Complex Variables Theory Appl. 15 (1990), no. 3, 193 – 196. · Zbl 0682.30021 [90] Karl-Goswin Grosse-Erdmann, Topologies on matrix spaces and universal matrices, Analysis 12 (1992), no. 1-2, 47 – 56. · Zbl 0764.40002 [91] K.-G. Grosse-Erdmann, Hypercyclic and chaotic weighted shifts, preprint. 5 · Zbl 0991.47013 [92] A. Gulisashvili and C. R. MacCluer, Linear chaos in the unforced quantum harmonic oscillator, J. Dynam. Systems Measurement Control 118 (1996), 337-338. Zbl 870:58057 5 · Zbl 0870.58057 [93] Don Hadwin, Eric Nordgren, Heydar Radjavi, and Peter Rosenthal, Orbit-reflexive operators, J. London Math. Soc. (2) 34 (1986), no. 1, 111 – 119. · Zbl 0624.47002 · doi:10.1112/jlms/s2-34.1.111 [94] Israel Halperin, Carol Kitai, and Peter Rosenthal, On orbits of linear operators, J. London Math. Soc. (2) 31 (1985), no. 3, 561 – 565. · Zbl 0578.47001 · doi:10.1112/jlms/s2-31.3.561 [95] M. Heins, A universal Blaschke product, Arch. Math. 6 (1955), 41-44. 4a,4b [96] Jacek Hejduk, Universal sequences in the space of real measurable functions, Zeszyty Nauk. Politech. Łódz. Mat. 21 (1989), 75 – 85 (1990) (English, with Russian and Polish summaries). · Zbl 0725.28004 [97] Domingo A. Herrero, Limits of hypercyclic and supercyclic operators, J. Funct. Anal. 99 (1991), no. 1, 179 – 190. · Zbl 0758.47016 · doi:10.1016/0022-1236(91)90058-D [98] Domingo A. Herrero, Hypercyclic operators and chaos, J. Operator Theory 28 (1992), no. 1, 93 – 103. · Zbl 0806.47020 [99] Domingo A. Herrero and Carol Kitai, On invertible hypercyclic operators, Proc. Amer. Math. Soc. 116 (1992), no. 3, 873 – 875. · Zbl 0780.47006 [100] Domingo A. Herrero and Zong Yao Wang, Compact perturbations of hypercyclic and supercyclic operators, Indiana Univ. Math. J. 39 (1990), no. 3, 819 – 829. · Zbl 0724.47009 · doi:10.1512/iumj.1990.39.39039 [101] G. Herzog, Universelle Funktionen, Diplomarbeit, Univ. Karlsruhe, Karlsruhe, 1988. 3e,4c [102] Gerd Herzog, On universal functions and interpolation, Analysis 11 (1991), no. 1, 21 – 26. · Zbl 0729.41007 · doi:10.1524/anly.1991.11.1.21 [103] Gerd Herzog, On zero-free universal entire functions, Arch. Math. (Basel) 63 (1994), no. 4, 329 – 332. · Zbl 0807.30014 · doi:10.1007/BF01189569 [104] Gerd Herzog, On a theorem of Seidel and Walsh, Period. Math. Hungar. 30 (1995), no. 3, 205 – 210. · Zbl 0846.30032 · doi:10.1007/BF01876619 [105] Gerd Herzog, On a universality of the heat equation, Math. Nachr. 188 (1997), 169 – 171. · Zbl 0886.35026 · doi:10.1002/mana.19971880110 [106] Gerd Herzog and Roland Lemmert, Über Endomorphismen mit dichten Bahnen, Math. Z. 213 (1993), no. 3, 473 – 477 (German). · Zbl 0793.47032 · doi:10.1007/BF03025732 [107] G. Herzog and R. Lemmert, On universal subsets of Banach spaces, Math. Z. 229 (1998), 615-619. CMP 99:06 2c · Zbl 0928.47003 [108] Gerd Herzog and Christoph Schmoeger, On operators \? such that \?(\?) is hypercyclic, Studia Math. 108 (1994), no. 3, 209 – 216. · Zbl 0818.47011 [109] M. Horváth, On multidimensional universal functions, Studia Sci. Math. Hungar. 22 (1987), no. 1-4, 75 – 78. · Zbl 0657.26005 [110] V. I. Ivanov, Representation of measurable functions by multiple trigonometric series, Dokl. Akad. Nauk SSSR 259 (1981), no. 2, 279 – 282 (Russian). [111] V. I. Ivanov, Representation of measurable functions by multiple trigonometric series, Trudy Mat. Inst. Steklov. 164 (1983), 100 – 123 (Russian). Orthogonal series and approximations of functions. · Zbl 0565.42006 [112] V. I. Ivanov, The coefficients of orthogonal universal series and zero series, Dokl. Akad. Nauk SSSR 272 (1983), no. 1, 19 – 23 (Russian). [113] V. I. Ivanov, Representation of functions by series in metric symmetric spaces without linear functionals, Dokl. Akad. Nauk SSSR 289 (1986), no. 3, 532 – 535 (Russian). [114] V. I. Ivanov, Representation of functions by series in metric symmetric spaces without linear functionals, Trudy Mat. Inst. Steklov. 189 (1989), 34 – 77 (Russian). Translated in Proc. Steklov Inst. Math. 1990, no. 4, 37 – 85; A collection of papers from the All-Union School on the Theory of Functions (Russian) (Dushanbe, 1986). [115] I. Joó, Note to a theorem of Talaljan on universal series and to a problem of Nikišin, Fourier analysis and approximation theory (Proc. Colloq., Budapest, 1976), Vol. I, Colloq. Math. Soc. János Bolyai, vol. 19, North-Holland, Amsterdam-New York, 1978, pp. 451 – 458. [116] I. Joó, On the divergence of eigenfunction expansions, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 32 (1989), 3 – 36 (1990). · Zbl 0734.42018 [117] István Joó, On a theorem of Miklós Horváth, Mat. Lapok 34 (1983/87), no. 4, 301 – 306 (1991) (Hungarian). · Zbl 0765.46012 [118] A. Kachenas and A. Laurinchikas, On Dirichlet series associated with some parabolic forms (Russian), Liet. Mat. Rink. 38 (1998), 82-97. English transl. in: Lithuanian Math. J. 38 (1998) (to appear). CMP 99:06 6 [119] Теория ортогонал$$^{\приме}$$ных рядов, Государств. Издат. Физ.-Мат. Лит., Мосцощ, 1958 (Руссиан). [120] J.-P. Kahane, General properties of Taylor series 1896-1996, J. Fourier Anal. Appl. 3 (1997), Special Issue, 907-911. CMP 98:09 4d [121] J.-P. Kahane, Baire theory in Fourier and Taylor series (Proc. Conf., Philadelphia, PA, 1996) (to appear). 4d [122] A. N. Kanatnikov, Limiting sets along sequences of compacta, Dokl. Akad. Nauk SSSR 253 (1980), no. 1, 14 – 17 (Russian). [123] A. N. Kanatnikov, Limit sets of meromorphic functions with respect to sequences of compacta, Izv. Akad. Nauk SSSR Ser. Mat. 48 (1984), no. 6, 1196 – 1213 (Russian). · Zbl 0563.30028 [124] A. A. Karatsuba and S. M. Voronin, The Riemann zeta-function, De Gruyter Expositions in Mathematics, vol. 5, Walter de Gruyter & Co., Berlin, 1992. Translated from the Russian by Neal Koblitz. · Zbl 0756.11022 [125] E. S. Katsoprinakis and M. Papadimitrakis, Extensions of a theorem of Marcinkiewicz-Zygmund and of Rogosinski’s formula and an application to universal Taylor series, Proc. Amer. Math. Soc. (to appear). CMP 99:01 4d · Zbl 0922.30002 [126] S. Ja. Havinson, Some problems concerning the completeness of systems, Soviet Math. Dokl. 2 (1961), 358 – 361. · Zbl 0129.07804 [127] S. Ja. Havinson, On approximation with account taken of the size of the coefficients of the approximants, Trudy Mat. Inst. Steklov. 60 (1961), 304 – 324 (Russian). [128] C. Kitai, Invariant closed sets for linear operators, Thesis, Univ. of Toronto, Toronto, 1982. 1a,1b,1c,2a,2b,2c,2d,5 [129] T. W. Körner, Universal trigonometric series with rapidly decreasing coefficients, Commutative harmonic analysis (Canton, NY, 1987) Contemp. Math., vol. 91, Amer. Math. Soc., Providence, RI, 1989, pp. 115 – 149. · doi:10.1090/conm/091/1002593 [130] V. Ya. Kozlov, On complete systems of orthogonal functions (Russian), Mat. Sb. (N.S.) 26(68) (1950), 351-364. 3c [131] V. G. Krotov, Representation of measurable functions by series in the Faber-Schauder system, and universal series, Dokl. Akad. Nauk SSSR 214 (1974), 1258 – 1261 (Russian). · Zbl 0303.42014 [132] V. G. Krotov, Universal Fourier series in the Faber-Schauder system, Vestnik Moskov. Univ. Ser. I Mat. Meh. 30 (1975), no. 4, 53 – 58 (Russian, with English summary). · Zbl 0349.42014 [133] V. G. Krotov, Representation of measurable functions by series in the Faber-Schauder system, and universal series, Izv. Akad. Nauk SSSR Ser. Mat. 41 (1977), no. 1, 215 – 229, 232 (Russian). · Zbl 0395.42010 [134] V. G. Krotov, On the smoothness of universal Marcinkiewicz functions and universal trigonometric series, Izv. Vyssh. Uchebn. Zaved. Mat. 8 (1991), 26 – 31 (Russian); English transl., Soviet Math. (Iz. VUZ) 35 (1991), no. 8, 24 – 28. · Zbl 0746.42005 [135] Charles W. Lamb, Representation of functions as limits of martingales, Trans. Amer. Math. Soc. 188 (1974), 395 – 405. · Zbl 0283.60052 [136] Antanas Laurinčikas, Distribution des valeurs de certaines séries de Dirichlet, C. R. Acad. Sci. Paris Sér. A-B 289 (1979), no. 2, A43 – A45 (French, with English summary). · Zbl 0423.10025 [137] Antanas Laurinčikas, Sur les séries de Dirichlet et les polynômes trigonométriques, Séminaire de Théorie des Nombres, 1978 – 1979, CNRS, Talence, 1979, pp. Exp. No. 24, 13 (French). [138] A. Laurinchikas, Distribution of values of generating Dirichlet series of multiplicative functions, Litovsk. Mat. Sb. 22 (1982), no. 1, 101 – 111 (Russian, with French and Lithuanian summaries). [139] A. Laurinchikas, The universality theorem, Litovsk. Mat. Sb. 23 (1983), no. 3, 53 – 62 (Russian, with French and Lithuanian summaries). [140] A. Laurinchikas, The universality theorem. II, Litovsk. Mat. Sb. 24 (1984), no. 2, 113 – 121 (Russian, with French and Lithuanian summaries). [141] A. Laurinchikas, On the universality of the Riemann zeta function, Liet. Mat. Rink. 35 (1995), no. 4, 502 – 507 (Russian, with Lithuanian summary); English transl., Lithuanian Math. J. 35 (1995), no. 4, 399 – 402 (1996). · Zbl 0867.11058 · doi:10.1007/BF02348827 [142] Antanas Laurinčikas, Limit theorems for the Riemann zeta-function, Mathematics and its Applications, vol. 352, Kluwer Academic Publishers Group, Dordrecht, 1996. · Zbl 0859.11053 [143] A. Laurinchikas, Universality of the Lerch zeta function, Liet. Mat. Rink. 37 (1997), no. 3, 367 – 375 (Russian, with Lithuanian summary); English transl., Lithuanian Math. J. 37 (1997), no. 3, 275 – 280 (1998). · Zbl 0938.11045 · doi:10.1007/BF02465359 [144] A. Laurinchikas, On the Lerch zeta function with rational parameters (Russian), Liet. Mat. Rink. 38 (1998), 113-124. English transl. in: Lithuanian Math. J. 38 (1998) (to appear). CMP 99:06 6 [145] A. Laurinčikas, On the Matsumoto zeta-function, Acta Arith. 84 (1998), 1-16. CMP 98:10 6 · Zbl 0904.11025 [146] A. Laurinčikas and K. Matsumoto, The universality of zeta-functions attached to certain cusp forms, preprint. 6 · Zbl 0974.11018 [147] F. León-Saavedra, Universal functions on the unit ball and the polydisk, Function spaces (Proc. Conf., Edwardsville, IL, 1998), Amer. Math. Soc., Providence, RI, 1999. 4a · Zbl 0937.32008 [148] Shamim I. Ansari, Existence of hypercyclic operators on topological vector spaces, J. Funct. Anal. 148 (1997), no. 2, 384 – 390. , https://doi.org/10.1006/jfan.1996.3093 Fernando León-Saavedra and Alfonso Montes-Rodríguez, Linear structure of hypercyclic vectors, J. Funct. Anal. 148 (1997), no. 2, 524 – 545. · Zbl 0999.47009 · doi:10.1006/jfan.1996.3084 [149] F. León-Saavedra and A. Montes-Rodríguez, Spectral theory and hypercyclic subspaces, Trans. Amer. Math. Soc. (to appear). 2a,2b,2d,4a,4c,5 · Zbl 0961.47003 [150] G. G. Lorentz, Bernstein polynomials, Univ. of Toronto Press, Toronto, 1953. 3a · Zbl 0051.05001 [151] Wolfgang Luh, Approximation analytischer Funktionen durch überkonvergente Potenzreihen und deren Matrix-Transformierten, Mitt. Math. Sem. Giessen Heft 88 (1970), i+56 (German). · Zbl 0231.30005 [152] Wolfgang Luh, Über die Anwendung von Übersummierbarkeit zur Approximation regulärer Funktionen, Topics in analysis (Colloq. Math. Anal., Jyväskylä, 1970) Springer, Berlin, 1974, pp. 260 – 267. Lecture Notes in Math., Vol. 419 (German). [153] Wolfgang Luh, Über die Summierbarkeit der geometrischen Reihe, Mitt. Math. Sem. Giessen Heft 113 (1974), 70 (German). · Zbl 0325.40003 [154] Wolfgang Luh, Über den Satz von Mergelyan, J. Approximation Theory 16 (1976), no. 2, 194 – 198. · Zbl 0336.30016 [155] W. Luh, On universal functions, Fourier analysis and approximation theory (Proc. Colloq., Budapest, 1976), Vol. II, Colloq. Math. Soc. János Bolyai, vol. 19, North-Holland, Amsterdam-New York, 1978, pp. 503 – 511. [156] W. Luh, Über cluster sets analytischer Funktionen, Acta Math. Acad. Sci. Hungar. 33 (1979), no. 1-2, 137 – 142 (German). Special issue dedicated to George Alexits on the occasion of his 80th birthday. · Zbl 0401.30030 · doi:10.1007/BF01903388 [157] Wolfgang Luh, Universalfunktionen in einfach zusammenhängenden Gebieten, Aequationes Math. 19 (1979), no. 2-3, 183 – 193 (German). · Zbl 0434.30021 · doi:10.1007/BF02189865 [158] Wolfgang Luh, Universal approximation properties of overconvergent power series on open sets, Analysis 6 (1986), no. 2-3, 191 – 207. · Zbl 0589.30003 [159] Wolfgang Luh, Holomorphic monsters, J. Approx. Theory 53 (1988), no. 2, 128 – 144. · Zbl 0669.30020 · doi:10.1016/0021-9045(88)90060-3 [160] Wolfgang Luh, Universal functions and conformal mappings, Serdica 19 (1993), no. 2-3, 161 – 166. · Zbl 0790.30005 [161] Wolfgang Luh, Entire functions with various universal properties, Complex Variables Theory Appl. 31 (1996), no. 1, 87 – 96. · Zbl 0869.30022 [162] Wolfgang Luh, Multiply universal holomorphic functions, J. Approx. Theory 89 (1997), no. 2, 135 – 155. · Zbl 0874.30029 · doi:10.1006/jath.1997.3036 [163] Wolfgang Luh, Valeri A. Martirosian, and Jürgen Müller, T-universal functions with lacunary power series, Acta Sci. Math. (Szeged) 64 (1998), no. 1-2, 67 – 79. · Zbl 0926.30001 [164] W. Luh, V. A. Martirosian, and J. Müller, Universal entire functions with gap power series, Indag. Math. (N.S.) (to appear). 4a,4b · Zbl 0914.30001 [165] S. Yu. Lukashenko and T. P. Lukashenko, The rate of growth of coefficients of universal series (Russian), Probability Theory, Theory of Random Processes, and Functional Analysis (Russian) (Proc. Conf., Moscow, 1984), 128-130, Moskov. Gos. Univ., Moscow, 1985. CMP 90:06 3c [166] C. R. MacCluer, Chaos in linear distributed systems, J. Dynam. Systems Measurement Control 114 (1992), 322-324. Zbl 778:93038 5 [167] G. R. MacLane, Sequences of derivatives and normal families, J. Analyse Math. 2 (1952/53), 72-87. 2a,4c · Zbl 0049.05603 [168] J. Marcinkiewicz, Sur les nombres dérivés, Fund. Math. 24 (1935), 305-308. Zbl 11:107 3b · Zbl 0011.10705 [169] F. Martínez-Giménez and A. Peris, Hypercyclic and chaotic backward shift operators on Köthe echelon spaces, preprint. 2c,2d,5 · Zbl 1070.47024 [170] Valentin Matache, Notes on hypercyclic operators, Acta Sci. Math. (Szeged) 58 (1993), no. 1-4, 401 – 410. · Zbl 0795.47002 [171] Valentin Matache, Spectral properties of operators having dense orbits, Topics in operator theory, operator algebras and applications (Timişoara, 1994) Rom. Acad., Bucharest, 1995, pp. 221 – 237. · Zbl 0866.47006 [172] Varughese Mathew, A note on hypercyclic operators on the space of entire sequences, Indian J. Pure Appl. Math. 25 (1994), no. 11, 1181 – 1184. · Zbl 0821.47019 [173] S. Mazurkiewicz, Sur l’approximation des fonctions continues d’une variable réelle par les sommes partielles d’une série de puissances, C. R. Soc. Sci. Lett. Varsovie Cl. III 30 (1937), 25-30. Zbl 17:204 1c,3a,4d · Zbl 0017.20406 [174] A. Melas and V. Nestoridis, Universality of Taylor series as a generic property of holomorphic functions, preprint. 3c,4d · Zbl 0985.30023 [175] A. Melas, V. Nestoridis, and I. Papadoperakis, Growth of coefficients of universal Taylor series and comparison of two classes of functions, J. Anal. Math. 73 (1997), 187-202. CMP 98:10 4d · Zbl 0894.30003 [176] D. Menchoff, Sur les séries trigonométriques universelles, C. R. (Dokl.) Acad. Sci. URSS (N.S.) 49 (1945), 79-82. 1c,3c · Zbl 0060.18504 [177] D. E. Men$$'$$shov, On the partial sums of trigonometric series (Russian), Mat. Sb. (N.S.) 20(62) (1947), 197-238. 1c,3c [178] D. Men$$'$$shov, On the convergence in measure of trigonometric series (Russian), Dokl. Akad. Nauk SSSR (N.S.) 59 (1948), 849-852. 3c [179] D. E. Men$$'$$shov, On convergence in measure of trigonometric series (Russian), Trudy Mat. Inst. Steklov. 32 (1950). English transl. in: Amer. Math. Soc. Transl. (1) 3 (1962), 196-270. 3c · Zbl 0058.05602 [180] D. E. Men$$'$$shov, On the limits of indeterminateness of partial sums of universal trigonometric series (Russian), Moskov. Gos. Univ. Uchen. Zap. 165 Mat. 7 (1954), 3-33. English transl. in: Amer. Math. Soc. Transl. (2) 111 (1978), 1-33. 3c [181] D. Men$$^{\prime}$$šov, On universal sequences of functions, Dokl. Akad. Nauk SSSR 151 (1963), 1283 – 1285 (Russian). [182] D. E. Men$$^{\prime}$$šov, Universal sequences of functions, Mat. Sb. (N.S.) 65 (107) (1964), 272 – 312 (Russian). · Zbl 0148.04102 [183] John Boris Miller, Generalized functions for the Laplace transform and universal approximants, Generalized functions and their applications (Varanasi, 1991) Plenum, New York, 1993, pp. 131 – 140. · Zbl 0840.46021 [184] T. L. Miller and V. G. Miller, Local spectral theory and orbits of operators, Proc. Amer. Math. Soc. 127 (1999), no. 4, 1029 – 1037. · Zbl 0911.47012 [185] V. G. Miller, Remarks on finitely hypercyclic and finitely supercyclic operators, Integral Equations Operator Theory 29 (1997), no. 1, 110 – 115. · Zbl 0902.47018 · doi:10.1007/BF01191482 [186] Alfonso Montes-Rodríguez, A note on Birkhoff open sets, Complex Variables Theory Appl. 30 (1996), no. 3, 193 – 198. · Zbl 0852.30021 [187] Alfonso Montes-Rodríguez, Banach spaces of hypercyclic vectors, Michigan Math. J. 43 (1996), no. 3, 419 – 436. · Zbl 0907.47023 · doi:10.1307/mmj/1029005536 [188] Alfonso Montes-Rodríguez, Vector spaces of universal functions, Complex methods in approximation theory (Almería, 1995) Monogr. Cienc. Tecnol., vol. 2, Univ. Almería, Almería, 1997, pp. 113 – 116. · Zbl 0915.47027 [189] Alfonso Montes-Rodríguez, Composition operators and hypercyclic vectors, Studies on composition operators (Laramie, WY, 1996) Contemp. Math., vol. 213, Amer. Math. Soc., Providence, RI, 1998, pp. 157 – 165. · Zbl 0901.47022 · doi:10.1090/conm/213/02857 [190] A. Montes-Rodríguez, A Birkhoff theorem for Riemann surfaces, Rocky Mountain J. Math. 28 (1998), 663-693. CMP 99:03 4a [191] Vassili Nestoridis, Universal Taylor series, Ann. Inst. Fourier (Grenoble) 46 (1996), no. 5, 1293 – 1306 (English, with English and French summaries). · Zbl 0865.30001 [192] V. Nestoridis, An extension of the notion of universal Taylor series, Computational Methods and Function Theory 1997 (Proc. Conf., Nicosia, 1997) (to appear). 3c,4d [193] J. Pál, Zwei kleine Bemerkungen, Tôhoku Math. J. 6 (1914/15), 42-43. JFM 45:634 1d,3a [194] G. Pál, On some generalisations of a theorem of Weierstrass (Hungarian), Math. Phys. Lapok 24 (1915), 243-247. JFM 45:634 3a [195] Marco Pavone, Chaotic composition operators on trees, Houston J. Math. 18 (1992), no. 1, 47 – 56. · Zbl 0773.47019 [196] A. Peris, Personal communications, 1998. 1b,2b [197] A. Peris, Chaotic polynomials on Fréchet spaces, Proc. Amer. Math. Soc. (to appear). CMP 98:09 2d,4c · Zbl 1042.46019 [198] N. B. Pogosjan, Representation of measurable functions by orthogonal series, Mat. Sb. (N.S.) 98(140) (1975), no. 1(9), 102 – 112, 158 – 159 (Russian). N. B. Pogosjan, Representation of measurable functions by bases in \?_{\?}[0,1], (\?\ge 2), Akad. Nauk Armjan. SSR Dokl. 63 (1976), no. 4, 205 – 209 (Russian, with Armenian summary). · Zbl 0349.40001 [199] N. B. Pogosjan, Representation of measurable functions by orthogonal series, Mat. Sb. (N.S.) 98(140) (1975), no. 1(9), 102 – 112, 158 – 159 (Russian). N. B. Pogosjan, Representation of measurable functions by bases in \?_{\?}[0,1], (\?\ge 2), Akad. Nauk Armjan. SSR Dokl. 63 (1976), no. 4, 205 – 209 (Russian, with Armenian summary). · Zbl 0349.40001 [200] V. Protopopescu and Y. Y. Azmy, Topological chaos for a class of linear models, Math. Models Methods Appl. Sci. 2 (1992), no. 1, 79 – 90. · Zbl 0770.58024 · doi:10.1142/S0218202592000065 [201] C. J. Read, The invariant subspace problem for a class of Banach spaces. II. Hypercyclic operators, Israel J. Math. 63 (1988), no. 1, 1 – 40. · Zbl 0782.47002 · doi:10.1007/BF02765019 [202] Axel Reich, Universelle Werteverteilung von Eulerprodukten, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II 1 (1977), 1 – 17 (German). · Zbl 0379.10025 [203] Axel Reich, Werteverteilung von Zetafunktionen, Arch. Math. (Basel) 34 (1980), no. 5, 440 – 451 (German). · Zbl 0431.10025 · doi:10.1007/BF01224983 [204] Axel Reich, Zur Universalität und Hypertranszendenz der Dedekindschen Zetafunktion, Abh. Braunschweig. Wiss. Ges. 33 (1982), 197 – 203 (German). · Zbl 0505.12018 [205] S. Rolewicz, On orbits of elements, Studia Math. 32 (1969), 17 – 22. · Zbl 0174.44203 [206] Héctor Salas, A hypercyclic operator whose adjoint is also hypercyclic, Proc. Amer. Math. Soc. 112 (1991), no. 3, 765 – 770. · Zbl 0748.47023 [207] Héctor N. Salas, Hypercyclic weighted shifts, Trans. Amer. Math. Soc. 347 (1995), no. 3, 993 – 1004. · Zbl 0822.47030 [208] H. Salas, Supercyclicity and weighted shifts, preprint. 5 · Zbl 0940.47005 [209] Christoph Schmoeger, On the norm-closure of the class of hypercyclic operators, Ann. Polon. Math. 65 (1997), no. 2, 157 – 161. · Zbl 0896.47013 [210] Ingo Schneider, Schlichte Funktionen mit universellen Approximationseigenschaften, Mitt. Math. Sem. Giessen 230 (1997), iv+72 (German). · Zbl 0870.30028 [211] W. Seidel and J. L. Walsh, On approximation by euclidean and non-euclidean translations of an analytic function, Bull. Amer. Math. Soc. 47 (1941), 916-920. 4a · Zbl 0028.40003 [212] A. I. Seleznev, On universal power series (Russian), Mat. Sb. (N.S.) 28(70) (1951), 453-460. 3a,4d [213] A. I. Seleznev and L. K. Dodynova, Some classes of universal series, Izv. Vysš. Učebn. Zaved. Matematika 12(187) (1977), 92 – 98 (Russian). · Zbl 0399.30029 [214] A. I. Seleznëv and L. K. Dodunova, On two theorems of A. F. Leont$$^{\prime}$$ev on the completeness of subsystems of Faber and Jacobi polynomials, Izv. Vyssh. Uchebn. Zaved. Mat. 4 (1982), 51 – 55 (Russian). · Zbl 0494.30005 [215] A. I. Seleznev, I. V. Motova, and V. A. Volohin, The completeness of systems of functions and universal series, Izv. Vysš. Učebn. Zaved. Matematika 11(186) (1977), 84 – 90 (Russian). · Zbl 0417.30007 [216] Joel H. Shapiro, Composition operators and classical function theory, Universitext: Tracts in Mathematics, Springer-Verlag, New York, 1993. · Zbl 0791.30033 [217] S. A. Shkarin, On the growth of \?-universal functions, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 6 (1993), 80 – 83 (1994) (Russian); English transl., Moscow Univ. Math. Bull. 48 (1993), no. 6, 49 – 51. [218] W. Sierpiński, Sur une série de puissances universelle pour les fonctions continues, Studia Math. 7 (1938), 45-48. Zbl 18:114 1d,3a [219] András Sövegjártó, A note on universal elements, Mat. Lapok 28 (1977/80), no. 4, 327 – 328 (Hungarian). [220] Karl R. Stromberg, Introduction to classical real analysis, Wadsworth International, Belmont, Calif., 1981. Wadsworth International Mathematics Series. · Zbl 0454.26001 [221] A. A. Talalyan, On the convergence almost everywhere of subsequences of partial sums of general orthogonal series (Russian), Akad. Nauk Armyan. SSR Izv. Fiz.-Mat. Estest. Tekhn. Nauki 10 (1957), no. 3, 17-34. 1d,3c,3d [222] A. A. Talaljan, Universal orthogonal series, Izv. Akad. Nauk Armyan. SSR. Ser. Fiz.-Mat. Nauk 12 (1959), no. 1, 27 – 42 (Russian, with Armenian summary). [223] A. A. Talaljan, On series of bases of \?_{\?} space which are universal with respect to permutations, Akad. Nauk Armyan. SSR. Dokl. 28 (1959), 145 – 150 (Russian, with Armenian summary). · Zbl 0089.27701 [224] A. A. Talaljan, On the convergence and summability almost everywhere of general orthogonal series, Izv. Akad. Nauk Armjan. SSR Ser. Fiz.-Mat. Nauk 13 (1960), no. 2, 31 – 61 (Russian, with Armenian summary). [225] A. A. Talaljan, Series universal with respect to rearrangement, Izv. Akad. Nauk SSSR. Ser. Mat. 24 (1960), 567 – 604 (Russian). [226] A. A. Talaljan, The representation of measurable functions by series, Russian Math. Surveys 15 (1960), no. 5, 75 – 136. · Zbl 0098.04203 · doi:10.1070/RM1960v015n05ABEH001115 [227] B. Thorpe and L. Tomm, Universal approximation by regular weighted means, Pacific J. Math. 117 (1985), no. 2, 443 – 455. · Zbl 0606.30002 [228] Li Xin Tian and Zeng Rong Liu, Nonwandering operators in infinite-dimensional linear spaces, Acta Math. Sci. (Chinese) 15 (1995), no. 4, 455 – 460 (Chinese, with Chinese summary). · Zbl 0900.47005 [229] Lixin Tian and Dianchen Lu, The property of nonwandering operator, Appl. Math. Mech. 17 (1996), no. 2, 151 – 156 (Chinese, with English and Chinese summaries); English transl., Appl. Math. Mech. 17 (1996), no. 2, 155 – 161. · Zbl 0848.47015 · doi:10.1007/BF00122311 [230] V. T. Todorov, Linear differential operators are transitive, Godishnik Vissh. Uchebn. Zaved. Prilozhna Mat. 21 (1985), no. 4, 17 – 25 (1986) (English, with Russian and Bulgarian summaries). · Zbl 0662.47026 [231] V. Todorov and O. Korov, An infinitely differentiable function, the set of derivatives of which is everywhere dense (Russian), Mathematics and Education in Mathematics (Bulgarian) (Proc. Conf., Sunny Beach, 1980), 91-94, B$$''$$lg. Akad. Nauk., Sofia, 1980. Zbl 573:26014 3e · Zbl 0573.26014 [232] L. Tomm and R. Trautner, A universal power series for approximation of measurable functions, Analysis 2 (1982), no. 1-4, 1 – 6. · Zbl 0568.28006 · doi:10.1524/anly.1982.2.14.1 [233] Hoang Tuĭ, The structure of measurable functions, Dokl. Akad. Nauk SSSR 126 (1959), 37 – 40 (Russian). · Zbl 0087.27401 [234] Tuĭ Hoang, The ”universal primitive” of J. Markusiewicz, Izv. Akad. Nauk SSSR. Ser. Mat. 24 (1960), 617 – 628 (Russian). [235] S. M. Voronin, A theorem on the distribution of values of the Riemann zeta-function, Dokl. Akad. Nauk SSSR 221 (1975), no. 4, 771 (Russian). · Zbl 0326.10035 [236] S. M. Voronin, A theorem on the ”universality” of the Riemann zeta-function, Izv. Akad. Nauk SSSR Ser. Mat. 39 (1975), no. 3, 475 – 486, 703 (Russian). · Zbl 0315.10037 [237] S. M. Voronin, Analytic properties of the Dirichlet generating series of arithmetic objects (Russian), Thesis, Moscow, 1977. 6 [238] S. M. Voronin, Distribution of zeros of certain Dirichlet series, Trudy Mat. Inst. Steklov. 163 (1984), 74 – 77 (Russian). International conference on analytical methods in number theory and analysis (Moscow, 1981). · Zbl 0555.10022 [239] G. F. Webb, Periodic and chaotic behavior in structured models of cell population dynamics, Recent developments in evolution equations (Glasgow, 1994) Pitman Res. Notes Math. Ser., vol. 324, Longman Sci. Tech., Harlow, 1995, pp. 40 – 49. · Zbl 0822.92016 [240] Paolo Zappa, On universal holomorphic functions, Boll. Un. Mat. Ital. A (7) 2 (1988), no. 3, 345 – 352 (English, with Italian summary). · Zbl 0658.30025
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