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Spectral approximation of Wiener-Hopf operators with almost periodic generating function

Author:
Roch, S  


Journal:
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION


Issue Date:
2000


Abstract(summary):

The paper deals with spectral approximation of Wiener-Hopf operators acting on LP-spaces by their finite sections. The generating functions of the Wiener-Hopf operators are supposed to be continuous plus almost periodic. While the usual spectra of the finite sections drastically fail to converge to the spectrum of the Wiener-Hopf operator, it turns out that other spectral approximants, viz. the pseudospectra and the numerical ranges, do converge perfectly. The proof requires a modified approach to the finite section method for Wiener-Hopf operators. This note generalizes results obtained by Bottcher, Grudsky and Silbermann for the case of continuous generating functions. AMS Subject Classification Number: Primary 65R20, Secondary 47G10.


Page:
241---253


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