Stability theory for semigroups using  (L^p,L^q)  Fourier multipliers

Stability theory for semigroups using  (L^p,L^q)  Fourier multipliers

Rozendaal, J. (Australian National University; Polish Academy of Sciences)
Veraar, M.C. (TU Delft Analysis)

2018

We study polynomial and exponential stability for C₀-semigroups using the recently developed theory of operator-valued (L^p,L^q) Fourier multipliers. We characterize polynomial decay of orbits of a C₀-semigroup in terms of the (L^p,L^q) 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.

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

http://resolver.tudelft.nl/uuid:208bd136-a733-4838-ab83-989ef59029f5

https://doi.org/10.1016/j.jfa.2018.06.015

2019-01-03

0022-1236

Journal of Functional Analysis, 275 (10), 2845-2894

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Institutional Repository

journal article

© 2018 J. Rozendaal, M.C. Veraar