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Generators of semigroups on Banach spaces inducing holomorphic semiflows

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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: \(\mathbb{D}\) → ℂ such that Af = Gf′ with maximal domain. The aim of the paper is the study of the reciprocal implication.

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Authors and Affiliations

  1. Institute of Applied Analysis, University of Ulm, Helmholtzstr. 18, D-89069, Ulm, Germany

    Wolfgang Arendt

  2. Université Paris Est Marne-la-Vallée, 5 bld. Descartes, Champs-sur-Marne, 77454, Marne-la-Vallée, Cedex 2, France

    Isabelle Chalendar

Authors
  1. Wolfgang Arendt
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  2. Isabelle Chalendar
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Correspondence to Isabelle Chalendar.

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Arendt, W., Chalendar, I. Generators of semigroups on Banach spaces inducing holomorphic semiflows. Isr. J. Math. 229, 165–179 (2019). https://doi.org/10.1007/s11856-018-1793-y

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  • DOI: https://doi.org/10.1007/s11856-018-1793-y

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