Stability theory for semigroups using  (Lp,Lq)  Fourier multipliers

Jan Rozendaal, Mark Veraar

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5 Citations (Scopus)
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We study polynomial and exponential stability for C0-semigroups using the recently developed theory of operator-valued (Lp,Lq) Fourier multipliers. We characterize polynomial decay of orbits of a C0-semigroup in terms of the (Lp,Lq) Fourier multiplier properties of its resolvent. Using this characterization we derive new polynomial decay rates which depend on the geometry of the underlying space. We do not assume that the semigroup is uniformly bounded, our results depend only on spectral properties of the generator. As a corollary of our work on polynomial stability we reprove and unify various existing results on exponential stability, and we also obtain a new theorem on exponential stability for positive semigroups.

Original languageEnglish
Pages (from-to)2845-2894
Number of pages50
JournalJournal of Functional Analysis
Issue number10
Publication statusPublished - 2018


  • C-semigroup
  • Fourier multipliers
  • Polynomial and exponential stability
  • Type and cotype

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