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arXiv · 1512.08886

$β$-admissibility of observation and control operators for hypercontractive semigroups

Birgit Jacob·Jonathan R. Partington·Sandra Pott·Andrew Wynn
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Abstract

We prove a Weiss conjecture on $β$-admissibility of control and observation operators for discrete and continuous $γ$-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 $γ=2$, which corresponds to the unweighted Bergman shift.

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Birgit Jacob, Jonathan R. Partington, Sandra Pott, Andrew Wynn. 2015-12-30. $β$-admissibility of observation and control operators for hypercontractive semigroups. https://arxiv.org/abs/1512.08886

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