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arXiv · 1810.11799

A Besov algebra calculus for generators of operator semigroups and related norm-estimates

Charles Batty·Alexander Gomilko·Yuri Tomilov
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Abstract

We construct a new bounded functional calculus for the generators of bounded semigroups on Hilbert spaces and generators of bounded holomorphic semigroups on Banach spaces. The calculus is a natural (and strict) extension of the classical Hille-Phillips functional calculus, and it is compatible with the other well-known functional calculi. It satisfies the standard properties of functional calculi, provides a unified and direct approach to a number of norm-estimates in the literature, and allows improvements of some of them.

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Charles Batty, Alexander Gomilko, Yuri Tomilov. 2019-10-17. A Besov algebra calculus for generators of operator semigroups and related norm-estimates. https://arxiv.org/abs/1810.11799

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