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arXiv · 1910.06369

The theory of Besov functional calculus: developments and applications to semigroups

Charles Batty·Alexander Gomilko·Yuri Tomilov
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Abstract

We extend and deepen the theory of functional calculus for semigroup generators, based on the algebra $\mathcal B$ of analytic Besov functions, which we initiated in a previous paper. In particular, we show that our construction of the calculus is optimal in several natural senses. Moreover, we clarify the structure of $\mathcal B$ and identify several important subspaces in practical terms. This leads to new spectral mapping theorems for operator semigroups and to wide generalisations of a number of basic results from semigroup theory.

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Charles Batty, Alexander Gomilko, Yuri Tomilov. 2019-10-14. The theory of Besov functional calculus: developments and applications to semigroups. https://arxiv.org/abs/1910.06369

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