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Approximation numbers = singular values

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Author

Summary, in English

This paper introduces a generalisation of the notion of singular value for Hilbert space operators to more general Banach spaces. It is shown that for a simple integral operator of Hardy type the singular values are the eigenvalues of a non-linear Sturm-Liouville equation and coincide with the approximation numbers of the operator. Finally, asymptotic formulas for the singular numbers are deduced. (c) 2006 Published by Elsevier B.V.

Publishing year

2007

Language

English

Pages

102-110

Publication/Series

Journal of Computational and Applied Mathematics

Volume

208

Issue

1

Document type

Journal article

Publisher

Elsevier

Topic

  • Mathematics

Keywords

  • Pruefer transform
  • eigenvalue
  • generalised trigonometric function
  • asymptotics
  • Bernstein width
  • Sturm-Liouville

Status

Published

ISBN/ISSN/Other

  • ISSN: 0377-0427