Sets non-thin at \infty in \Bbb C ^m, and the growth of sequences of entire functions of genus zero

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dc.creatorTuyen, Truong Trung
dc.date2007-10-14
dc.date2007-12-13
dc.date.accessioned2026-07-07T08:48:45Z
dc.date.available2026-07-07T08:48:45Z
dc.descriptionIn 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)=0 for 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 $E\backslash A$ is non-thin at $\infty$, if $E\subset \Bbb C^m$ and $F\subset \Bbb C^n$ are closed sets non-thin at $\infty$ then $E\times F\subset \Bbb C^m\times \Bbb C^n$ is non-thin at $\infty$ (see Lemma \ref{Lem1}). Then we explore the properties of non-thin at $\infty$ sets and apply this to extend the results in \cite{mul-yav} and \cite{trong-tuyen}.
dc.description12 pages. We added some more results
dc.identifierhttps://arxiv.org/abs/0710.2671
dc.identifierhttp://arxiv.org/abs/0710.2671
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/144054
dc.subjectComplex Variables
dc.subjectDynamical Systems
dc.subject31B05, 32A15, 31A22
dc.titleSets non-thin at \infty in \Bbb C ^m, and the growth of sequences of entire functions of genus zero
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