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Convolution type operators on cones and their finite sections

✍ Scribed by Helena Mascarenhas; Bernd Silbermann

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
322 KB
Volume
278
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

This paper is concerned with finite sections of convolution type operators defined on cones, whose symbol is the Fourier transform of an integrable function on ℝ^2^. The algebra of these finite sections satisfies a set of axioms (standard model) that ensures some asymptotic properties like the convergence of the condition numbers, singular values, ε‐pseudospectrum and also gives a relation between the singular values of an approximation sequence and the kernel dimensions of a set of associated operators. This approach furnishes a method to determine whether a Fredholm convolution operator on a cone is invertible. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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