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Asymptotic formulas for Toeplitz determinants. (English) Zbl 0409.47018

##### MSC:
 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators 42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series 47B10 Linear operators belonging to operator ideals (nuclear, $$p$$-summing, in the Schatten-von Neumann classes, etc.)
##### Keywords:
Toeplitz Determinants; Strong Szego Limit Theorem
Full Text:
##### References:
 [1] E. W. Barnes, The theory of the G-function, Quart. J. Pure Appl. Math. 31 (1900), 264-313. · JFM 30.0389.02 [2] H. Bateman, Higher transcendental functions, Vol. 1, Bateman Manuscript Project (A. Erdélyi, Editor), McGraw-Hill, New York, 1953. MR 15, 419. [3] A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Tables of integral transforms. Vol. I, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1954. Based, in part, on notes left by Harry Bateman. · Zbl 0055.36401 [4] Ralph Philip Boas Jr., Entire functions, Academic Press Inc., New York, 1954. · Zbl 0058.30201 [5] Herbert Buchholz, The confluent hypergeometric function with special emphasis on its applications, Translated from the German by H. Lichtblau and K. Wetzel. Springer Tracts in Natural Philosophy, Vol. 15, Springer-Verlag New York Inc., New York, 1969. · Zbl 0169.08501 [6] M. E. Fisher and R. E. Hartwig, Toeplitz determinants. Some applications, theorems and conjectures, Adv. Chem. Phys. 15 (1968), 333-353. [7] I. C. Gohberg and M. G. Krein, Introduction to the theory of linear nonselfadjoint operators in Hilbert space; English transl., Transl. Math. Monographs, vol. 18, Amer. Math. Soc., Providence, R. I., 1968. MR 39 #7447. [8] Ulf Grenander and Gabor Szegö, Toeplitz forms and their applications, California Monographs in Mathematical Sciences, University of California Press, Berkeley-Los Angeles, 1958. · Zbl 0080.09501 [9] I. I. Hirschman Jr., On a formula of Kac and Achiezer, J. Math. Mech. 16 (1966), 167 – 196. · Zbl 0154.37203 [10] I. I. Hirschman Jr., On a theorem of Szegö, Kac, and Baxter, J. Analyse Math. 14 (1965), 225 – 234. · Zbl 0141.07001 · doi:10.1007/BF02806390 · doi.org [11] I. I. Hirschman Jr., Recent developments in the theory of finite Toeplitz operators, Advances in probability and related topics, Vol. 1, Dekker, New York, 1971, pp. 103 – 167. [12] A. Lenard, Some remarks on large Toeplitz determinants, Pacific J. Math. 42 (1972), 137 – 145. · Zbl 0255.42005 [13] G. Szegö, Orthogonal polynomials, Amer. Math. Soc. Colloq. Publ., vol. 23, rev. ed., Providence, R. I., 1959. MR 21 #5029. · Zbl 0089.27501 [14] E. T. Whittaker and G. N. Watson, A course of modern analysis, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1996. An introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions; Reprint of the fourth (1927) edition. · JFM 53.0180.04 [15] Harold Widom, Asymptotic behavior of block Toeplitz matrices and determinants, Advances in Math. 13 (1974), 284 – 322. , https://doi.org/10.1016/0001-8708(74)90072-3 Harold Widom, Asymptotic behavior of block Toeplitz matrices and determinants. II, Advances in Math. 21 (1976), no. 1, 1 – 29. · Zbl 0344.47016 · doi:10.1016/0001-8708(76)90113-4 · doi.org [16] Harold Widom, Toeplitz determinants with singular generating functions, Amer. J. Math. 95 (1973), 333 – 383. · Zbl 0275.45006 · doi:10.2307/2373789 · doi.org
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