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Asymptotic dependence of the extreme eigenvalues of truncated Toeplitz matrices on the rate at which the symbol attains its extremum

Author(s): A. Yu. Novosel'tsev; I. B. Simonenko
Translated by: V. V. Kapustin
Original publication: Algebra i Analiz, tom 16 (2004), vypusk 4.
Journal: St. Petersburg Math. J. 16 (2005), 713-718.
MSC (2000): Primary 47B35
Posted: June 23, 2005
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References:

1.
S. Serra, On the extreme eigenvalues of Hermitian (block) Toeplitz matrices, Linear Algebra Appl. 270 (1998), 109-129. MR 1484077 (98k:15034)

2.
G. Szego, Beiträge zur Theorie der Toeplitzschen Formen. I, II, Math. Z. 6 (1920), 167-202; 9 (1921), 167-190.

3.
-, On certain Hermitian forms associated with the Fourier series of a positive function, Comm. Sém. Math. Univ. Lund 1952, Tome Suppl., 228-238. MR 0051961 (14:553d)

4.
U. Grenander and G. Szego, Toeplitz forms and their applications, 2nd ed., Chelsea Publishing Co., New York, 1984. MR 0890515 (88b:42031)

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Additional Information:

A. Yu. Novosel'tsev
Affiliation: Department of Mathematics and Mechanics, Rostov State University, Zorge 5, Rostov-on-Don 344090, Russia

I. B. Simonenko
Affiliation: Department of Mathematics and Mechanics, Rostov State University, Zorge 5, Rostov-on-Don 344090, Russia

DOI: 10.1090/S1061-0022-05-00875-7
PII: S 1061-0022(05)00875-7
Keywords: Toeplitz matrix, eigenvalue asymptotics
Received by editor(s): 31/JUL/2003
Posted: June 23, 2005
Copyright of article: Copyright 2005, American Mathematical Society

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