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Analytic Semigroups of Holomorphic Mappings and Composition Operators

Abstract

In this manuscript we provide a review on the classical and resent results related to the problem of analytic extension in parameter for a semigroup of holomorphic self-mappings of the unit ball in a complex Banach space and its relation to the linear continuous semigroup of composition operators.

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Acknowledgements

The second author gratefully acknowledges the support of the German Research Society (DFG), Grant TA 289/12-1, and wishes to thank the University of Potsdam for the invitation and hospitality. The publication was also prepared with the support of the “RUDN University Programm 5-100”.

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Correspondence to Mark Elin.

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Communicated by Stephan Ruscheweyh.

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Elin, M., Shoikhet, D. & Tarkhanov, N. Analytic Semigroups of Holomorphic Mappings and Composition Operators. Comput. Methods Funct. Theory 18, 269–294 (2018). https://doi.org/10.1007/s40315-017-0227-x

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  • DOI: https://doi.org/10.1007/s40315-017-0227-x

Keywords

  • Non-linear semigroups
  • Composition operators
  • Analytic extension
  • Holomorphic mappings

Mathematics Subject Classification

  • Primary 37L05
  • Secondary 47H20
  • 47B33