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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.
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author
; ; and
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
Birkhäuser Verlag
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
2016-04-01 10:58:40
date last changed
2022-04-04 23:04:08
@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}},
  keywords     = {{Gram matrix; Thin interpolating sequence; Schatten-p class}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{93--99}},
  publisher    = {{Birkhäuser Verlag}},
  series       = {{Archiv der Mathematik}},
  title        = {{Thin sequences and the Gram matrix}},
  url          = {{http://dx.doi.org/10.1007/s00013-014-0667-8}},
  doi          = {{10.1007/s00013-014-0667-8}},
  volume       = {{103}},
  year         = {{2014}},
}