Acta mathematica scientia,Series B ›› 2017, Vol. 37 ›› Issue (2): 355-367.doi: 10.1016/S0252-9602(17)30007-3

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APPLICATION OF HOLOMORPHIC INVARIANTS IN REPRODUCING KERNEL

Lishuang PAN1,2, An WANG2   

  1. 1. School of Mathematics and Physics, Handan University, Handan 056005, China;
    2. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
  • Received:2015-08-04 Revised:2016-07-09 Online:2017-04-25 Published:2017-04-25
  • Supported by:

    This work is supported by the National Natural Science Foundation of China (11371257) and Colleges and Universities Science and Technology Research Foundation of Hebei Province (QN2016304).

Abstract:

We use holomorphic invariants to calculate the Bergman kernel for generalized quasi-homogeneous Reinhardt-Hartogs domains. In addition, we present a complete orthonormal basis for the Bergman space on bounded Reinhardt-Hartogs domains.

Key words: Generalized quasi-homogeneous domain, Bergman kernel function, holomorphic invariant

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