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AAK-type theorems for Hankel operators on weighted spaces

Andersson, Fredrik LU ; Carlsson, Marcus LU and Perfekt, Karl-Mikael (2015) In Bulletin des Sciences Mathématiques 139(2). p.184-197
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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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Singular vectors, Schmidt pairs, Henkel operators, AAK theory
in
Bulletin des Sciences Mathématiques
volume
139
issue
2
pages
184 - 197
publisher
Gauthier-Villars
external identifiers
  • wos:000351791100004
  • scopus:84924520174
ISSN
0007-4497
DOI
10.1016/j.bulsci.2014.08.008
language
English
LU publication?
yes
id
92b22307-4d90-4225-8732-28ec3f8af718 (old id 5293720)
date added to LUP
2016-04-01 15:00:06
date last changed
2022-04-30 05:31:49
@article{92b22307-4d90-4225-8732-28ec3f8af718,
  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.}},
  author       = {{Andersson, Fredrik and Carlsson, Marcus and Perfekt, Karl-Mikael}},
  issn         = {{0007-4497}},
  keywords     = {{Singular vectors; Schmidt pairs; Henkel operators; AAK theory}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{184--197}},
  publisher    = {{Gauthier-Villars}},
  series       = {{Bulletin des Sciences Mathématiques}},
  title        = {{AAK-type theorems for Hankel operators on weighted spaces}},
  url          = {{http://dx.doi.org/10.1016/j.bulsci.2014.08.008}},
  doi          = {{10.1016/j.bulsci.2014.08.008}},
  volume       = {{139}},
  year         = {{2015}},
}