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arXiv · 2407.09323

Improved polynomial decay for unbounded semigroups

Chenxi Deng·Jan Rozendaal·Mark Veraar
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Abstract

We obtain polynomial decay rates for $C_{0}$-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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Chenxi Deng, Jan Rozendaal, Mark Veraar. 2024-07-12. Improved polynomial decay for unbounded semigroups. https://doi.org/10.1007/s00028-024-01028-8

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