Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Asymptotic formulas for Toeplitz determinants
HTML articles powered by AMS MathViewer

by Estelle Basor PDF
Trans. Amer. Math. Soc. 239 (1978), 33-65 Request permission

Abstract:

The object of this paper is to find an asymptotic formula for determinants of finite dimensional Toeplitz operators generated by a class of functions with singularities. The formula is a generalization of the Strong Szegö Limit Theorem.
References
    E. W. Barnes, The theory of the G-function, Quart. J. Pure Appl. Math. 31 (1900), 264-313. H. Bateman, Higher transcendental functions, Vol. 1, Bateman Manuscript Project (A. Erdélyi, Editor), McGraw-Hill, New York, 1953. MR 15, 419.
  • A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Tables of integral transforms. Vol. I, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1954. Based, in part, on notes left by Harry Bateman. MR 0061695
  • Ralph Philip Boas Jr., Entire functions, Academic Press, Inc., New York, 1954. MR 0068627
  • Herbert Buchholz, The confluent hypergeometric function with special emphasis on its applications, Springer Tracts in Natural Philosophy, Vol. 15, Springer-Verlag New York, Inc., New York, 1969. Translated from the German by H. Lichtblau and K. Wetzel. MR 0240343, DOI 10.1007/978-3-642-88396-5
  • M. E. Fisher and R. E. Hartwig, Toeplitz determinants. Some applications, theorems and conjectures, Adv. Chem. Phys. 15 (1968), 333-353. I. C. Gohberg and M. G. Kreǐn, 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.
  • Ulf Grenander and Gabor Szegö, Toeplitz forms and their applications, California Monographs in Mathematical Sciences, University of California Press, Berkeley-Los Angeles, 1958. MR 0094840
  • I. I. Hirschman Jr., On a formula of Kac and Achiezer, J. Math. Mech. 16 (1966), 167–196. MR 0208279, DOI 10.1512/iumj.1967.16.16012
  • I. I. Hirschman Jr., On a theorem of Szegö, Kac, and Baxter, J. Analyse Math. 14 (1965), 225–234. MR 177250, DOI 10.1007/BF02806390
  • 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. MR 0305130
  • A. Lenard, Some remarks on large Toeplitz determinants, Pacific J. Math. 42 (1972), 137–145. MR 331106, DOI 10.2140/pjm.1972.42.137
  • G. Szegö, Orthogonal polynomials, Amer. Math. Soc. Colloq. Publ., vol. 23, rev. ed., Providence, R. I., 1959. MR 21 #5029.
  • 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. MR 1424469, DOI 10.1017/CBO9780511608759
  • Harold Widom, Asymptotic behavior of block Toeplitz matrices and determinants, Advances in Math. 13 (1974), 284–322. MR 409511, DOI 10.1016/0001-8708(74)90072-3
  • Harold Widom, Toeplitz determinants with singular generating functions, Amer. J. Math. 95 (1973), 333–383. MR 331107, DOI 10.2307/2373789
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 47B35, 42A56
  • Retrieve articles in all journals with MSC: 47B35, 42A56
Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 239 (1978), 33-65
  • MSC: Primary 47B35; Secondary 42A56
  • DOI: https://doi.org/10.1090/S0002-9947-1978-0493480-X
  • MathSciNet review: 0493480