$\beta$-admissibility of observation and control operators for hypercontractive semigroups
Analysis of PDEs
2016-01-15 v1 Functional Analysis
Abstract
We prove a Weiss conjecture on -admissibility of control and observation operators for discrete and continuous -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 , which corresponds to the unweighted Bergman shift.
Cite
@article{arxiv.1512.08886,
title = {$\beta$-admissibility of observation and control operators for hypercontractive semigroups},
author = {Birgit Jacob and Jonathan R. Partington and Sandra Pott and Andrew Wynn},
journal= {arXiv preprint arXiv:1512.08886},
year = {2016}
}