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Besov spaces in theory of approximation. (English) Zbl 0193.41401

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[1] H. Berens,Approximationssätze für Halbgruppenoperatoren in intermediären Räumen Schriftenreihe, Math. Inst. Univ. Münster. 32 (1964). · Zbl 0124.06604
[2] – –,Interpotationsmethoden zur Behandlung von Approximationsprozessen auf Banachräumen, Lecture Notes in Math. 64, 1968 Springer. · Zbl 0164.43801
[3] L. Bers, F. John, andM. Schechter,Partial differential epuations, Interscience (1964).
[4] Besov, O. V., Investigation of a family of function spaoes in connection with theorems of imbedding and extension, Trudy. Mat. Inst. Steklov, 60, 42-81 (1961)
[5] Butzer, P. L., Uber den Approximationsgrad des Identitätsoperator durch Halbgruppen von linearen Operatoren und Anwendungen auf die Theorie der singulären Integrale, Math. Ann., 133, 410-425 (1957) · Zbl 0081.33403
[6] Butzer, P. L., Fourier-transform methods in the theory of approximation, Arch. Rational Mech. Anal., 5, 390-415 (1960) · Zbl 0107.32101
[7] Butzer, P. L.; Berens, H., Semi-Groups of Operators and Approximation (1967), Berlin: Springer, Berlin · Zbl 0164.43702
[8] Favard, J., Sur l’approximation des fonction d’une variable réelle, Colloque d’Anale. Hann. Publ. C.N.R.S. Paris, 15, 97-110 (1949) · Zbl 0040.02803
[9] G. W. Hedstrom,The rate of convergence of some difference schemas, Department of Mathematics, Chalmers Institute of Technology and the University of Göteborg, (1967).
[10] – –,The rate of convergence of parabolic difference schemas with constant coefficients, To appear.
[11] Holmstedt, T., Interpolation d’espaces quasi-normés, C.R. Acad. Sci. Paris., 264, 242-244 (1967) · Zbl 0145.16401
[12] Hömander, L., Estimates for translation invariant operators in L, Acta Math., 104, 93-140 (1960)
[13] – –,On the Riesz’ means of spectral functions and eigen-function expansions for elliptic differential operators.
[14] Hömander, L., The spectral function of an elliptic operator, Acta Math., 121, 3-4, 192-218 (1968)
[15] J. L. Lions, L. I. Lizorkin andS. M. Nikolskij,Integral representations and isomorphism properties of some classes of function, Ann Scuola Norm Sup. Pisa, pp. 127-178 (1965). · Zbl 0151.18001
[16] Löfström, J., On certain interpolation spaces related to goneralized semi-groups, Math. Scand., 16, 41-54 (1965) · Zbl 0128.35104
[17] Löfström, J., Some Theorems on Interpolation Spaces with Applications to Approximation in L, Math. Ann., 172, 176-196 (1967) · Zbl 0186.45701
[18] – –,On the rate of convergence of difference schemas for parabolic initial-value problems and of singular integrals, To appear. in Proc. of the Conference on Abstract Spaces and Approximation, Oberwohlfach 1968, Birkhäuser.
[19] R. J. Messel,Das Saturationsproblem für mehrdimensionale singuläre Integrale und seine Lösung mit Hilfe der Fourier-Transformation, Dissertation. TH Aachen 1955, pp. 1-145.
[20] J. Peetre,Espaces d’interpolation, generalizations, applications, Rend. Seminar Mat. Fis. Milano34 (1964). · Zbl 0151.17902
[21] – –,Applications de la théorie des espaces d’interpolation dans l’Analyse Harmonique, Ricerche Mat.15 (1966). · Zbl 0154.15302
[22] – –,Operators of finite Riesz order, Dept. of Math. Lund (1966) (In Swedish).
[23] – –,Reflections about Besov spaces, lecture notes, Department of Mathematics, Lund (1966) (In Swedish).
[24] Peetre, J., Sur tes espaces de Besov, C.R. Acad. Sci. Paris Sér. A, 264, 281-283 (1967) · Zbl 0145.16206
[25] J. Peetre andV. Thomée,On the rate of convergence for discrete initial-value problems, Department of Mathematics, Chalmers Institute of Technology and the University of Göteborg (1967). · Zbl 0172.13902
[26] Richtmyer, R. D.; Morton, K. W., Difference methods for initial value problems (1967), New York: Interscience, New York · Zbl 0155.47502
[27] Shapiro, H. S., A Tauberian Theorem Related to Approximation Theory, Acta Math., 120, 3-4, 279-292 (1968) · Zbl 0165.13801
[28] S. Sjöstrand,On the Riesz means of the Schrödinger equation, To appear in Ann. Scuola Norm. sup. Pisa. · Zbl 0201.14901
[29] S. Spanne,Operational calculi and interpolation, To appear.
[30] Stein, E. M., Localization and summability of multiple Fourier series, Acta Math., 100, 93-147 (1958) · Zbl 0085.28401
[31] Strang, W. G., Polynomial approximation of Bernstein type, Trans. Amer. Mat. Soc., 105, 525-535 (1962) · Zbl 0119.28703
[32] Thomée, V., Parabolic difference operators, Mat. Scand., 19, 177-207 (1966) · Zbl 0171.13804
[33] Thomée, V., Stability of Difference Schemas in the Maximum-Norm, Journ. Diff. Eq., 1, 3, 273-292 (1965) · Zbl 0259.65086
[34] S. Wainger,Special trigonometric serîes in k-dimensions, Memoirs Amer. Math. Soc.59 (1965). · Zbl 0136.36601
[35] Widlund, O. B., Stability of parabolic difference schemas in the maximum norm, Numer. Math., 8, 186-202 (1966) · Zbl 0173.44805
[36] – –,On the rate of convergence for parabolic schemas I, II. To appear, in Procedings from AMS’s symposium of Applied Math. Durham N.C. April 1968.
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