Limiting sets of eigenvalues and singular values of Toeplitz matrices

Article type: Research Article

Authors: Roch, Steffen | Silbermann, Bernd

Affiliations: Technische Universität Chemnitz, Fachbereich Mathematik, PSF 964, D 09009 Chemnitz, Germany

Note: [] Correspondence to: S. Roch, Technische Universität Chemnitz, Fachbereich Mathematik, PSF 964, D 09009 Chemnitz, Germany.

Abstract: The paper is devoted to the asymptotic behavior of the eigenvalues and singular values of Toeplitz and Hankel matrices with piecewise continuous generating functions. The central result is a norm stability theorem for sequences of matrices belonging to a Banach algebra of Toeplitz operators. This theorem applies to derive a complete description of the partial and the uniform limiting set of the eigenvalues and the singular values of the matrices under consideration.

DOI: 10.3233/ASY-1994-8306

Journal: Asymptotic Analysis, vol. 8, no. 3, pp. 293-309, 1994