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Mathematics > Functional Analysis

Title: Generators of semigroups on Banach spaces inducing holomorphic semiflows

Abstract: Let $A$ be the generator of a $C_0$-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 $G:{\mathbb D}\to{\mathbb C}$ such that $Af=Gf'$ with maximal domain. The aim of the paper is the study of the reciprocal implication.
Comments: 14 pages, Accepted, Israel Journal of Mathematics 2018
Subjects: Functional Analysis (math.FA)
MSC classes: 30D05, 47D03, 47B33
Cite as: arXiv:1803.06552 [math.FA]
  (or arXiv:1803.06552v1 [math.FA] for this version)

Submission history

From: Isabelle Chalendar [view email]
[v1] Sat, 17 Mar 2018 18:37:15 GMT (13kb)