Eigenvalues for Infinitesimal Generators of Semigroups of Composition Operators

Fuente: arXiv
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Main Authors: Kourou, Maria, Theodosiadis, Eleftherios K., Zarvalis, Konstantinos
Format: Preprint
Published: 2025
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author Kourou, Maria
Theodosiadis, Eleftherios K.
Zarvalis, Konstantinos
author_facet Kourou, Maria
Theodosiadis, Eleftherios K.
Zarvalis, Konstantinos
contents We study the eigenvalues for infinitesimal generators of semigroups of composition operators acting on Hardy spaces, Bergman spaces, and the Dirichlet space. Such semigroups are induced by semigroups of holomorphic functions. Depending on the type of the holomorphic semigroup and the Euclidean geometry of its Koenigs domain, we find containment relations as well as sufficient conditions for the characterization of the point spectrum of the induced infinitesimal generator. For the Dirichlet space we study all types of non-elliptic semigroups whereas for the Hardy and Bergman spaces we work on parabolic semigroups extending the work of Betsakos in the hyperbolic case.
format Preprint
id arxiv_https___arxiv_org_abs_2508_00666
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Eigenvalues for Infinitesimal Generators of Semigroups of Composition Operators
Kourou, Maria
Theodosiadis, Eleftherios K.
Zarvalis, Konstantinos
Complex Variables
Functional Analysis
47B33, 47D06, 30D05
We study the eigenvalues for infinitesimal generators of semigroups of composition operators acting on Hardy spaces, Bergman spaces, and the Dirichlet space. Such semigroups are induced by semigroups of holomorphic functions. Depending on the type of the holomorphic semigroup and the Euclidean geometry of its Koenigs domain, we find containment relations as well as sufficient conditions for the characterization of the point spectrum of the induced infinitesimal generator. For the Dirichlet space we study all types of non-elliptic semigroups whereas for the Hardy and Bergman spaces we work on parabolic semigroups extending the work of Betsakos in the hyperbolic case.
title Eigenvalues for Infinitesimal Generators of Semigroups of Composition Operators
topic Complex Variables
Functional Analysis
47B33, 47D06, 30D05
url https://arxiv.org/abs/2508.00666