On checking Lp-admissibility for parabolic control systems

Philip Preußler; Felix L. Schwenninger

doi:10.48550/arXiv.2404.06250

On checking Lp-admissibility for parabolic control systems

Philip Preußler, Felix L. Schwenninger

Research output: Working paper › Preprint › Academic

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Abstract

In this note we discuss the difficulty of verifying Lp-admissibility for p≠2 -- that even manifests in the presence of a self-adjoint semigroup generator on a Hilbert space -- and survey tests for Lp-admissibility of given control operators. These tests are obtained by virtue of either mapping properties of boundary trace operators, yielding a characterization of admissibility via abstract interpolation spaces; or through Laplace--Carleson embeddings, slightly extending results from Jacob, Partington and Pott to a class of systems which are not necessarily diagonal with respect to sequence spaces. Special focus is laid on illustrating the theory by means of examples based on the heat equation on various domains.

Original language	English
Publisher	ArXiv.org
Number of pages	32
DOIs	https://doi.org/10.48550/arXiv.2404.06250
Publication status	Published - 9 Apr 2024

Keywords

math.OC
math.FA
93B28, 93C05, 93C25, 47N70

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10.48550/arXiv.2404.06250Licence: Other

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On Checking L^p-Admissibility for Parabolic Control Systems
Preußler, P. & Schwenninger, F. L., 24 Jun 2024, Systems Theory and PDEs: Open Problems, Recent Results, and New Directions. Springer, p. 219-256 38 p. (Trends in Mathematics; vol. Part F3446).
Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic › peer-review

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Cite this

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M3 - Preprint

BT - On checking Lp-admissibility for parabolic control systems

PB - ArXiv.org

ER -

On checking Lp-admissibility for parabolic control systems

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On Checking Lp-Admissibility for Parabolic Control Systems

Cite this

On Checking L^p-Admissibility for Parabolic Control Systems