Generators of semigroups on Banach spaces inducing holomorphic semiflows
W. Arendt, I. Chalendar

TL;DR
This paper investigates the relationship between generators of semigroups of composition operators on Banach spaces of analytic functions and holomorphic semiflows, focusing on the conditions under which the generator can be represented as a differential operator with a holomorphic symbol.
Contribution
It establishes conditions under which generators of composition semigroups induce holomorphic semiflows, extending the understanding of their structure on Banach spaces.
Findings
Characterization of generators inducing holomorphic semiflows
Conditions for the differential operator representation
Extension of known results on composition operators
Abstract
Let be the generator of a -semigroup on a Banach space of analytic functions on the open unit disc. If consists of composition operators, then there exists a holomorphic function such that with maximal domain. The aim of the paper is the study of the reciprocal implication.
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Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Banach Space Theory · Algebraic and Geometric Analysis
