The theory of Besov functional calculus: developments and applications to semigroups - Batty, CJK; Gomilko, A; Tomilov, Y (Elsevier, 2021)
We extend and deepen the theory of functional calculus for semigroup generators, based on the algebra 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 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.