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β-admissibility of observation operators for hypercontractive semigroups

Jacob, Birgit; Partington, Jonathan R.; Pott, Sandra LU and Wynn, Andrew (2017) In Journal of Evolution Equations
Abstract

We prove a Weiss conjecture on (Formula presented.)-admissibility of observation operators for discrete and continuous (Formula presented.)-hypercontractive semigroups of operators, by representing them in terms of shifts on weighted Bergman spaces and using a reproducing kernel thesis for Hankel operators. Particular attention is paid to the case (Formula presented.), which corresponds to the unweighted Bergman shift.

Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
epub
subject
keywords
Admissibility, Bergman space, Dilation theory, Hankel operator, Hypercontraction, Reproducing kernel thesis, Semigroup system
in
Journal of Evolution Equations
pages
18 pages
publisher
Birkhaüser
external identifiers
  • scopus:85021188906
ISSN
1424-3199
DOI
10.1007/s00028-017-0395-1
language
English
LU publication?
yes
id
643f218e-47fb-4533-93b5-29fb3244a747
date added to LUP
2017-07-11 12:43:36
date last changed
2018-01-07 12:11:13
@article{643f218e-47fb-4533-93b5-29fb3244a747,
  abstract     = {<p>We prove a Weiss conjecture on (Formula presented.)-admissibility of observation operators for discrete and continuous (Formula presented.)-hypercontractive semigroups of operators, by representing them in terms of shifts on weighted Bergman spaces and using a reproducing kernel thesis for Hankel operators. Particular attention is paid to the case (Formula presented.), which corresponds to the unweighted Bergman shift.</p>},
  author       = {Jacob, Birgit and Partington, Jonathan R. and Pott, Sandra and Wynn, Andrew},
  issn         = {1424-3199},
  keyword      = {Admissibility,Bergman space,Dilation theory,Hankel operator,Hypercontraction,Reproducing kernel thesis,Semigroup system},
  language     = {eng},
  month        = {06},
  pages        = {18},
  publisher    = {Birkhaüser},
  series       = {Journal of Evolution Equations},
  title        = {β-admissibility of observation operators for hypercontractive semigroups},
  url          = {http://dx.doi.org/10.1007/s00028-017-0395-1},
  year         = {2017},
}