Improved polynomial decay for unbounded semigroups

Deng, C.; Rozendaal, J.; Veraar, M.C.

Improved polynomial decay for unbounded semigroups

Journal article (2024)

Authors

C. Deng Beijing Delft Institute of Intelligent Science and Technology , Analysis -

J. Rozendaal Polish Academy of Sciences, Analysis -

M.C. Veraar Analysis -

Research Group

Analysis () (TU Delft)

Fourier multiplier C-semigroup 42B37 46B20 Polynomial stability Primary 47D06 Secondary 35B40

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Published Date

2024

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Analysis

Abstract

We obtain polynomial decay rates for C₀-semigroups, assuming that the resolvent grows polynomially at infinity in the complex right half-plane. Our results do not require the semigroup to be uniformly bounded, and for unbounded semigroups, we improve upon previous results by, for example, removing a logarithmic loss on non-Hilbertian Banach spaces.

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