Spectra of multilevel toeplitz matrices: Advanced theory via simple matrix relationships

We consider the eigenvalue and singular-value distributions for m-level Toeplitz matrices generated by a complex-valued periodic function ƒ of m real variables. We show that familiar formulations for ƒ L ∞ (due to Szegő and others) can be preserved so long as f L 1, and what is more, with G. Weyl�...

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Bibliographic Details
Published inLinear algebra and its applications Vol. 270; no. 1; pp. 15 - 27
Main Authors Tyrtyshnikov, E.E., Zamarashkin, N.L.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.02.1998
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Summary:We consider the eigenvalue and singular-value distributions for m-level Toeplitz matrices generated by a complex-valued periodic function ƒ of m real variables. We show that familiar formulations for ƒ L ∞ (due to Szegő and others) can be preserved so long as f L 1, and what is more, with G. Weyl's definitions just a bit changed. In contrast to other approaches, the one we follow is based on simple matrix relationships.
ISSN:0024-3795
1873-1856
DOI:10.1016/S0024-3795(97)80001-8