A class of quasicontractive semigroups acting on Hardy and Dirichlet space

C. Avicou; I. Chalendar; J. R. Partington

A class of quasicontractive semigroups acting on Hardy and Dirichlet space

Functional Analysis 2015-02-20 v2 Complex Variables

Authors: C. Avicou , I. Chalendar , J. R. Partington

Abstract

This paper provides a complete characterization of quasicontractive $C_0$ -semigroups on Hardy and Dirichlet space with a prescribed generator of the form $Af=Gf'$ . We show that such semigroups are semigroups of composition operators and we give simple sufficient and necessary condition on $G$ . Our techniques are based on ideas from semigroup theory, such as the use of numerical ranges.

Keywords

quasicontractive semigroups Hardy space Dirichlet space composition operators generator numerical ranges semigroup theory

Cite

@article{arxiv.1502.00314,
  title  = {A class of quasicontractive semigroups acting on Hardy and Dirichlet space},
  author = {C. Avicou and I. Chalendar and J. R. Partington},
  journal= {arXiv preprint arXiv:1502.00314},
  year   = {2015}
}

Comments

28 pages. Revised version, to appear in J. Evolution Equations

A class of quasicontractive semigroups acting on Hardy and Dirichlet space

Abstract

Keywords

Cite

Comments

Related papers