Analyticity and compactness of semigroups of composition operators

作者：Avicou C; Chalendar I; Partington J R^*

来源：Journal of Mathematical Analysis and Applications, 2016, 437(1): 545-560.

DOI：10.1016/j.jmaa.2016.01.010

• Analytic semigroup
• Compact semigroup
• Semiflow
• Hardy space
• Dirichlet space
• Composition operators

This paper provides a complete characterisation of quasicontractive groups and analytic C-0-semigroups on Hardy and Dirichlet space on the unit disc with a prescribed generator of the form Af = Gf'. In the analytic case we also give a complete characterisation of immediately compact semigroups. When the analyticity fails, we obtain sufficient conditions for compactness and membership in the trace class. Finally, we analyse the case where the unit disc is replaced by the right-half plane, where the results are drastically different.

• 出版日期2016-5-1