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On the distribution singular values of Toeplitz matrices
Author(s):
Milutin
R.
Dostanic
Journal:
Proc. Amer. Math. Soc.
130
(2002),
1755-1764.
MSC (2000):
Primary 47B10, 47B35
Posted:
October 24, 2001
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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:
- 1.
- E.L. Basor, ``Trace formulas for Toeplitz Matrices with Piecewise continuous Symbols'', Journal of Mathematical Analysis and Applications, 120 (1986), 25-38. MR 88a:47027
- 2.
- A. Bötcher and B. Silberman,``Invertibility and Asymptotics of Toeplitz Matrices'', Berlin, Akademie-Verlag 1983. MR 85g:47037
- 3.
- I. C. Gohberg and M. G. Krein, ``Introduction to the theory of linear nonselfadjoint operators'', Translation of the Math. Monographs, Vol. 18, Amer. Math. Soc., Providence, R.I, 1969. MR 39:7447
- 4.
- L.M. Libkind, ``The asymptotic behavior of the eigenvalues of Toeplitz forms'', Math. Notes, 11 (1972), 97-101.
- 5.
- P.I. Lizorkin, ``Estimates of trigonometric integrals and the Bernstein inequality for fractional derivatives'' Izv. Akad. Nauk SSSR, Ser. Mat. T29 (1965), 109-126.
- 6.
- H. Widom ``A trace formula for Wiener-Hopf operators'' J. Operator Theory, 8 (1982), 279-298. MR 84e:47038
- 7.
- H. Widom, ``On the singular values of Toeplitz matrices'' Zeitschrift fur Analysis und Ihre Anwendungen, 8 (1989), no. 3, 221-229. MR 90k:47058
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Additional Information:
Milutin
R.
Dostanic
Affiliation:
Matematicki Fakultet, University of Belgrade, Studentski trg 16, 11000 Belgrade, Yugoslavia
Email:
domi@matf.bg.ac.yu
DOI:
10.1090/S0002-9939-01-06259-1
PII:
S 0002-9939(01)06259-1
Keywords:
Toeplitz matrices,
singular values
Received by editor(s):
April 26, 2000
Received by editor(s) in revised form:
December 15, 2000
Posted:
October 24, 2001
Communicated by:
David R. Larson
Copyright of article:
Copyright
2001,
American Mathematical Society
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