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arXiv · 1708.02259

On generators of $C_0$-semigroups of composition operators

Eva A. Gallardo-Gutiérrez·Dmitry Yakubovich
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Abstract

Avicou, Chalendar and Partington proved that an (unbounded) operator $(Af)=G\cdot f'$ on the classical Hardy space generates a $C_0$ semigroup of composition operators if and only if it generates a quasicontractive semigroup. Here we prove that if such an operator $A$ generates a $C_0$ semigroup, then it is automatically a semigroup of composition operators, so that the condition of quasicontractivity of the semigroup in the cited result is not necessary. Our result applies to a rather general class of Banach spaces of analytic functions in the unit disc.

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Eva A. Gallardo-Gutiérrez, Dmitry Yakubovich. 2017-08-07. On generators of $C_0$-semigroups of composition operators. https://doi.org/10.1007/s11856-018-1815-9

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