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

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

2002-10-25

arxiv.org/abs/math/0210399v1

Mathematics

Complex Variables

14 pages. To appear in Positivity

Scientific paper

A domain $G\subset \bar\mathbb C$ is the domain of holomorphy of the
generating function of a P\'olya 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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