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Thin sequences and the Gram matrix

Gorkin, Pamela; McCarthy, John E.; Pott, Sandra LU and Wick, Brett D. (2014) In Archiv der Mathematik 103(1). p.93-99
Abstract
We provide a new proof of Volberg's Theorem characterizing thin interpolating sequences as those for which the Gram matrix associated to the normalized reproducing kernels is a compact perturbation of the identity. In the same paper, Volberg characterized sequences for which the Gram matrix is a compact perturbation of a unitary as well as those for which the Gram matrix is a Schatten-2 class perturbation of a unitary operator. We extend this characterization from 2 to p, where 2 <= p <= infinity.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Gram matrix, Thin interpolating sequence, Schatten-p class
in
Archiv der Mathematik
volume
103
issue
1
pages
93 - 99
publisher
Birkhaüser
external identifiers
  • wos:000339969000010
  • scopus:84905489807
ISSN
0003-889X
DOI
10.1007/s00013-014-0667-8
language
English
LU publication?
yes
id
bc4dc828-76bd-4b58-bb54-8730d6b8a7a0 (old id 4667883)
date added to LUP
2014-09-24 16:08:03
date last changed
2017-11-12 03:14:26
@article{bc4dc828-76bd-4b58-bb54-8730d6b8a7a0,
  abstract     = {We provide a new proof of Volberg's Theorem characterizing thin interpolating sequences as those for which the Gram matrix associated to the normalized reproducing kernels is a compact perturbation of the identity. In the same paper, Volberg characterized sequences for which the Gram matrix is a compact perturbation of a unitary as well as those for which the Gram matrix is a Schatten-2 class perturbation of a unitary operator. We extend this characterization from 2 to p, where 2 &lt;= p &lt;= infinity.},
  author       = {Gorkin, Pamela and McCarthy, John E. and Pott, Sandra and Wick, Brett D.},
  issn         = {0003-889X},
  keyword      = {Gram matrix,Thin interpolating sequence,Schatten-p class},
  language     = {eng},
  number       = {1},
  pages        = {93--99},
  publisher    = {Birkhaüser},
  series       = {Archiv der Mathematik},
  title        = {Thin sequences and the Gram matrix},
  url          = {http://dx.doi.org/10.1007/s00013-014-0667-8},
  volume       = {103},
  year         = {2014},
}