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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the distribution singular values of Toeplitz matrices
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by Milutin R. Dostanić PDF
Proc. Amer. Math. Soc. 130 (2002), 1755-1764 Request permission

Abstract:

We prove a second order formula concerning distribution of singular values of Toeplitz matrices in some cases when conditions of the H. Widom Theorem are not satisfied.
References
  • E. L. Basor, Trace formulas for Toeplitz matrices with piecewise continuous symbols, J. Math. Anal. Appl. 120 (1986), no. 1, 25–38. MR 861905, DOI 10.1016/0022-247X(86)90201-5
  • Albrecht Böttcher and Bernd Silbermann, Invertibility and asymptotics of Toeplitz matrices, Mathematical Research, vol. 17, Akademie-Verlag, Berlin, 1983. MR 734173
  • I. C. Gohberg and M. G. Kreĭn, Introduction to the theory of linear nonselfadjoint operators, Translations of Mathematical Monographs, Vol. 18, American Mathematical Society, Providence, R.I., 1969. Translated from the Russian by A. Feinstein. MR 0246142, DOI 10.1090/mmono/018
  • L.M. Libkind, “The asymptotic behavior of the eigenvalues of Toeplitz forms”, Math. Notes, 11 (1972), 97-101.
  • P.I. Lizorkin, “Estimates of trigonometric integrals and the Bernstein inequality for fractional derivatives” Izv. Akad. Nauk SSSR, Ser. Mat. T29 (1965), 109-126.
  • Harold Widom, A trace formula for Wiener-Hopf operators, J. Operator Theory 8 (1982), no. 2, 279–298. MR 677415
  • H. Widom, On the singular values of Toeplitz matrices, Z. Anal. Anwendungen 8 (1989), no. 3, 221–229 (English, with German and Russian summaries). MR 1023115, DOI 10.4171/ZAA/350
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Additional Information
  • Milutin R. Dostanić
  • Affiliation: Matematicki Fakultet, University of Belgrade, Studentski trg 16, 11000 Belgrade, Yugoslavia
  • Email: domi@matf.bg.ac.yu
  • Received by editor(s): April 26, 2000
  • Received by editor(s) in revised form: December 15, 2000
  • Published electronically: October 24, 2001
  • Communicated by: David R. Larson
  • © Copyright 2001 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 130 (2002), 1755-1764
  • MSC (2000): Primary 47B10, 47B35
  • DOI: https://doi.org/10.1090/S0002-9939-01-06259-1
  • MathSciNet review: 1887023