Abstract
This paper is aimed at the stable computation of the partial indices of regular and smooth matrix functions defined on the complex unit circle under special emphasis on the speed of convergence. A crucial role plays the k-splitting property of appropriately constructed block matrices, namely modified finite sections A n of Toeplitz operators. It is proved that the singular values s k (A n ) tend with high speed to zero as n → ∞ for smooth regular functions where k stands for the splitting number.
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Dedicated to G. S. Litvinchuk on the occasion of his seventieth birthday
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Silbermann, B. (2003). How to Compute the Partial Indices of a Regular and Smooth Matrix-Valued Function?. In: Samko, S., Lebre, A., dos Santos, A.F. (eds) Factorization, Singular Operators and Related Problems. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0227-0_19
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DOI: https://doi.org/10.1007/978-94-017-0227-0_19
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6333-5
Online ISBN: 978-94-017-0227-0
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