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Analytic Semigroups of Holomorphic Mappings and Composition Operators

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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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Authors and Affiliations

  1. Department of Mathematics, Ort Braude College, 21982, Karmiel, Israel

    Mark Elin

  2. Holon Institute of Technology and People’s Friendship University of Russia (RUDN University), Golomb 52, 5810201, Holon, Israel

    David Shoikhet

  3. Institute of Mathematics, University of Potsdam, Karl-Liebknecht-Str. 24/25, Golm, 14476, Potsdam, Germany

    Nikolai Tarkhanov

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  1. Mark Elin
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  2. David Shoikhet
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  3. Nikolai Tarkhanov
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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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