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A class of quasicontractive semigroups acting on Hardy and Dirichlet space (1502.00314v2)
Published 1 Feb 2015 in math.FA and math.CV
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.