AAK-type theorems for Hankel operators on weighted spaces
Författare
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.
Avdelning/ar
Publiceringsår
2015
Språk
Engelska
Sidor
184-197
Publikation/Tidskrift/Serie
Bulletin des Sciences Mathématiques
Volym
139
Issue
2
Dokumenttyp
Artikel i tidskrift
Förlag
Gauthier-Villars
Ämne
- Computer Vision and Robotics (Autonomous Systems)
- Mathematics
Nyckelord
- Singular vectors
- Schmidt pairs
- Henkel operators
- AAK theory
Status
Published
ISBN/ISSN/Övrigt
- ISSN: 0007-4497