Acta mathematica scientia,Series B ›› 2015, Vol. 35 ›› Issue (1): 71-78.doi: 10.1016/S0252-9602(14)60139-9

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ON THE VALIRON’S THEOREM IN THE POLYDISK

WANG Gang,DENG FangWen   

  1. Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China University of Chinese Academy of Sciences, Beijing 10039, China Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
  • Received:2014-03-18 Revised:2014-07-01 Online:2015-01-20 Published:2015-01-20
  • Supported by:

    Supported by the National Natural Science Foundation of China (11271359).

Abstract:

In this paper, we discuss the Valiron’s theorem in the unit polydisk DN. We prove that for a holomorphic map ' : DN → DN satisfying some regular conditions, there exists a holomorphic map  : DN → H and a constant > 0 such that  ? ' = 1  . It is based on the extension of Julia-Wolff-Carath´eodory (JWC) theorem of D in the polydisk

Key words: Valiron’s theorem, Julia-Wolff-Carath´eodory, polydisk

CLC Number: 

  • 32H50
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