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Silbermann, Bernd : Modified Finite Sections for Toeplitz Operators and their singular values

Silbermann, Bernd : Modified Finite Sections for Toeplitz Operators and their singular values

Author(s):
Silbermann, Bernd
Title:
Modified Finite Sections for Toeplitz Operators and their singular values
Preprint series:
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 6, 2002
Mathematics Subject Classification:
47B35 [ Toeplitz operators, Hankel operators, Wiener-Hopf operators ]
65F20 [ Overdetermined systems, pseudoinverses ]
Abstract:
The topic of the paper ist the study of modified finite sections of Toeplitz operators and their singular values. We prove the splitting property for the singular values and consider two important consequences. We show that the kernel dimensions of a Fredholm Toeplitz operator with piecewise continuous matrix-valued generating function can be extracted from the singular values behavior of the modified sections. Secondly, we generalize the results on asymptotic Moore-Penrose invertibility of Heinig and Hellinger to piecewise continuous generating functions.
Keywords:
Toeplitz operators, singular values, finite sections, Moore-Penrose invertibility
Language:
English
Publication time:
8 / 2002