Generators of semigroups on Banach spaces inducing holomorphic semiflows

2018/03/17 by Wolfgang Arendt, Arendt, W., Isabelle Chalendar +1 · 1 citation
Mathematics · #30D05 #47B33 #47D03 #Advanced Banach Space Theory #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1803.06552

openalex publication_date 2018/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A be the generator of a C₀-semigroup T on a Banach space of analytic functions on the open unit disc. If T consists of composition operators, then there exists a holomorphic function G:\mathbb D→\mathbb C such that Af=Gf' with maximal domain. The aim of the paper is the study of the reciprocal implication.

Cited by

• Eigenvalues for Infinitesimal Generators of Semigroups of Composition Operators

Related

• Generators of C₀-semigroups of weighted composition operators
• Generation of subordinated holomorphic semigroups via Yosida's theorem
• Weighted composition semigroups on Banach spaces of holomorphic functions
• Semigroups of weighted composition operators on spaces of holomorphic functions
• Criteria for Analyticity of Multidimensionally Subordinate Semigroups