β-admissibility of observation operators for hypercontractive semigroups
(2018) In Journal of Evolution Equations 18(1). p.153-170- 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:
https://lup.lub.lu.se/record/643f218e-47fb-4533-93b5-29fb3244a747
- author
- Jacob, Birgit ; Partington, Jonathan R. ; Pott, Sandra LU and Wynn, Andrew
- organization
- publishing date
- 2018-03
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Admissibility, Bergman space, Dilation theory, Hankel operator, Hypercontraction, Reproducing kernel thesis, Semigroup system
- in
- Journal of Evolution Equations
- volume
- 18
- issue
- 1
- pages
- 153 - 170
- publisher
- Birkhäuser Verlag
- 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
- 2022-04-25 01:17:24
@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}}, keywords = {{Admissibility; Bergman space; Dilation theory; Hankel operator; Hypercontraction; Reproducing kernel thesis; Semigroup system}}, language = {{eng}}, number = {{1}}, pages = {{153--170}}, publisher = {{Birkhäuser Verlag}}, 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}}, doi = {{10.1007/s00028-017-0395-1}}, volume = {{18}}, year = {{2018}}, }