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Parametric Representation of Infinitesimal Generators on the Polydisk

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Abstract

In this paper, analogues of the Berkson–Porta formula for the infinitesimal generators of one-parameter semigroup of holomorphic self-maps on the polydisk are obtained. We give a necessary and sufficient condition for a holomorphic vector field to be an infinitesimal generator which improves the theorem given by Contreras, de Fabritiis and Díaz-Madrigal.

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Authors and Affiliations

  1. Department of Mathematics, Tianjin University, Tianjin, 300072, People’s Republic of China

    Ren-Yu Chen & Ze-Hua Zhou

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  1. Ren-Yu Chen
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  2. Ze-Hua Zhou
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Correspondence to Ren-Yu Chen.

Additional information

Communicated by Simeon Reich.

This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 11401426, 11371276).

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Chen, RY., Zhou, ZH. Parametric Representation of Infinitesimal Generators on the Polydisk. Complex Anal. Oper. Theory 10, 725–735 (2016). https://doi.org/10.1007/s11785-015-0450-2

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  • DOI: https://doi.org/10.1007/s11785-015-0450-2

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