Balayage of measures and subharmonic functions to a system of rays. I. The classical case
作者: B. N. KhabibullinA. V. Shmeleva
刊名: St. Petersburg Mathematical Journal, 2019, Vol.31 (1), pp.117-156
来源数据库: American Mathematical Society Journal
DOI: 10.1090/spmj/1589
关键词: Entire functionSequence of zerosSubharmonic functionRiesz measureBalayage
原始语种摘要: Classical balayage of measures and subharmonic functions to a system $ S$ of rays with common origin on the complex plane $ \mathbb{C}$ is developed. For a subharmonic function $ v$ on $ \mathbb{C}$, this makes it possible to construct another subharmonic function on $ \mathbb{C}$ that is harmonic outside $ S$ and coincides with $ v$ on $ S$. This is applied to the study of the relationship between the growth of an entire function on $ S$ and the distributions of its zeros, the investigation of conditions for completely regular growth of entire and subharmonic functions, the analysis of noncompleteness for systems of exponentials in spaces of holomorphic functions in nonconvex unbounded open sets that narrow down near infinity. The present text is the first part of the paper, and it...
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  • system 
  • subharmonic 分谐波
  • construction 构造
  • function 函数
  • measures 层组
  • second 
  • necessary 必要的
  • developed 开发
  • between 在中间
  • growth 生长