On Checking Lp-Admissibility for Parabolic Control Systems

Philip Preußler; Felix L. Schwenninger

doi:10.1007/978-3-031-64991-2_9

On Checking L^p-Admissibility for Parabolic Control Systems

Philip Preußler^*, Felix L. Schwenninger

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic › peer-review

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Abstract

In this chapter we discuss the difficulty of verifying L^p-admissibility for p≠2—which even manifests in the presence of a self-adjoint semigroup generator on a Hilbert space—and survey tests for L^p-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 [31] 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
Title of host publication	Systems Theory and PDEs
Subtitle of host publication	Open Problems, Recent Results, and New Directions
Publisher	Springer
Pages	219-256
Number of pages	38
DOIs	https://doi.org/10.1007/978-3-031-64991-2_9
Publication status	Published - 24 Jun 2024
Event	Workshop on Systems Theory and PDEs 2022 - TU Bergakademie Freiberg, Freiberg, Germany Duration: 18 Jul 2022 → 22 Jul 2022

Publication series

Name	Trends in Mathematics
Volume	Part F3446
ISSN (Print)	2297-0215
ISSN (Electronic)	2297-024X

Workshop

Workshop	Workshop on Systems Theory and PDEs 2022
Abbreviated title	WOSTAP
Country/Territory	Germany
City	Freiberg
Period	18/07/22 → 22/07/22

Keywords

2025 OA procedure
Infinite-dimensional system
Laplace–Carleson embedding
Weiss conjecture
Admissible operator

Access to Document

10.1007/978-3-031-64991-2_9

978-3-031-64991-2_9Final published version, 970 KBLicence: Taverne

Cite this

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