Final state observability in Banach spaces with applications to subordination and semigroups induced by Lévy processes

Research output: Contribution to journalResearch articleContributedpeer-review


  • Dennis Gallaun - , Hamburg University of Technology (Author)
  • Jan Meichsner - , Research Group for Astronomy, FernUniversität in Hagen (Author)
  • Christian Seifert - , Hamburg University of Technology (Author)


This paper generalizes the abstract method of proving an observability estimate by combining an uncertainty principle and a dissipation estimate. 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 Levy processes.


Original languageEnglish
Pages (from-to)1102-1121
Number of pages20
JournalEvolution Equations and Control Theory
Issue number4
Publication statusPublished - Aug 2023

External IDs

WOS 000930545000001
unpaywall 10.3934/eect.2023002
Mendeley 9368cde1-ffbe-35a8-9667-f802ae69278d
ORCID /0000-0002-9900-7864/work/142256396



  • Banach space, C-semigroups, Final state observability estimate, fractional powers, null-controllability, C-0 -semigroups, Fractional powers, Null controllability, C0-semigroups