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AAK-type theorems for Hankel operators on weighted spaces

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Author

Summary, in English

We consider weighted sequence spaces on N with increasing weights. Given a fixed integer k and a Hankel operator Gamma on such a space, we show that the kth singular vector generates an analytic function with precisely k zeroes in the unit disc, in analogy with the classical AAK-theory of Hardy spaces. We also provide information on the structure of the singular spectrum for Hankel operators, applicable for instance to operators on the Dirichlet and Bergman spaces. Finally, we show by example that the connection between the classical AAK-theorem and rational approximation fails for the Dirichlet space. (c) 2014 Elsevier Masson SAS. All rights reserved.

Publishing year

2015

Language

English

Pages

184-197

Publication/Series

Bulletin des Sciences Mathématiques

Volume

139

Issue

2

Document type

Journal article

Publisher

Gauthier-Villars

Topic

  • Computer Vision and Robotics (Autonomous Systems)
  • Mathematics

Keywords

  • Singular vectors
  • Schmidt pairs
  • Henkel operators
  • AAK theory

Status

Published

ISBN/ISSN/Other

  • ISSN: 0007-4497