AAK-type theorems for Hankel operators on weighted spaces

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Abstract

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.

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Subject classification (UKÄ) – MANDATORY

  • Computer Vision and Robotics (Autonomous Systems)
  • Mathematics

Keywords

  • Singular vectors, Schmidt pairs, Henkel operators, AAK theory
Original languageEnglish
Pages (from-to)184-197
JournalBulletin des Sciences Mathématiques
Volume139
Issue number2
Publication statusPublished - 2015
Publication categoryResearch
Peer-reviewedYes