The theory of Besov functional calculus: developments and applications to semigroups
arXiv:1910.06369
Abstract
We extend and deepen the theory of functional calculus for semigroup generators, based on the algebra 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 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.
arXiv comment51 pages. This is a version of the paper to appear in Journal of Functional Analysis