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  4. Final state observability in banach spaces with applications to subordination and semigroups induced by lévy processes
 
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Final state observability in banach spaces with applications to subordination and semigroups induced by lévy processes

Publikationstyp
Journal Article
Date Issued
2023-08
Sprache
English
Author(s)
Gallaun, Dennis  orcid-logo
Meichsner, Jan  
Seifert, Christian  orcid-logo
Institut
Mathematik E-10  
TORE-URI
http://hdl.handle.net/11420/15220
Journal
Evolution equations and control theory  
Volume
12
Issue
4
Start Page
1102
End Page
1121
Citation
Evolution Equations and Control Theory 12 (4): 1102-1121 (2023-08)
Publisher DOI
10.3934/eect.2023002
Scopus ID
2-s2.0-85151458589
This paper generalizes the abstract method of proving an observ-ability estimate by combining an uncertainty principle and a dissipation es-timate. In these estimates we allow for a large class of growth/decay rates satisfying an integrability condition. In contrast to previous results, we use an iterative argument which enables us to give an asymptotically sharp estimate for the observation constant and which is explicit in the model parameters. We give two types of applications where the extension of the growth/decay rates naturally appear. By exploiting subordination techniques we show how the dissipation estimate of a semigroup transfers to subordinated semigroups. Furthermore, we apply our results to semigroups related to Lévy processes.
Subjects
Banach space
C -semigroups 0
Final state observability estimate
fractional powers
null-controllability
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