# Domains of Holomorphy of Generating Functions of Pólya Frequency Sequences of Finite Order*

Domains of Holomorphy of Generating Functions of Pólya Frequency Sequences of Finite Order* 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,∂G)ε∂G. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# Domains of Holomorphy of Generating Functions of Pólya Frequency Sequences of Finite Order*

, Volume 8 (1) – Oct 21, 2004
12 pages

/lp/springer_journal/domains-of-holomorphy-of-generating-functions-of-p-lya-frequency-d0wVD5k78d
Publisher
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1023/B:POST.0000023234.55851.68
Publisher site
See Article on Publisher Site

### 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,∂G)ε∂G.

### Journal

PositivitySpringer Journals

Published: Oct 21, 2004

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