Sets non-thin at infty in Bbb C ^m, and the growth of sequences of entire functions of genus zero - Mathematics > Complex VariablesReport as inadecuate




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Abstract: In this paper we define the notion of non-thin at $\infty$ as follows: Let$E$ be a subset of $\Bbb C^m$. For any $R>0$ define $E R=E\cap \{z\in \Bbb C ^m:|z|\leq R\}$. We say that $E$ is non-thin at $\infty$ if\lim {R\to\infty}V {E R}z=0for all $z\in \Bbb C^m$, where $V E$ is the pluricomplex Green function of$E$.This definition of non-thin at $\infty$ has good properties: If $E\subset\Bbb C^m$ is non-thin at $\infty$ and $A$ is pluripolar then $E\backslash A$ isnon-thin at $\infty$, if $E\subset \Bbb C^m$ and $F\subset \Bbb C^n$ are closedsets non-thin at $\infty$ then $E\times F\subset \Bbb C^m\times \Bbb C^n$ isnon-thin at $\infty$ see Lemma ef{Lem1}.Then we explore the properties of non-thin at $\infty$ sets and apply this toextend the results in \cite{mul-yav} and \cite{trong-tuyen}.



Author: Truong Trung Tuyen

Source: https://arxiv.org/







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