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Domains of holomorphy of generating functions of Polya frequency sequences of finite order

Maria Teresa Alzugaray
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Abstract

A domain $G\subset \bar\mathbb C$ is the domain of holomorphy of the generating function of a Pólya frequency sequence of order $r$ if and only if it satisfies the following conditions: (A) $G$ contains the point $z=0$, (B) $G$ is symmetric with respect to the real axis, (C) $T=dist(0,\partial G)\in \partial G$.

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Maria Teresa Alzugaray. 2002-10-25. Domains of holomorphy of generating functions of Polya frequency sequences of finite order. https://arxiv.org/abs/math/0210399

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