Kuttner's problem and a Pólya type criterion

for characteristic functions

Author:
Tilmann Gneiting

Journal:
Proc. Amer. Math. Soc. **128** (2000), 1721-1728

MSC (1991):
Primary 42A82, 60E10; Secondary 42A24, 42A38

DOI:
https://doi.org/10.1090/S0002-9939-99-05200-4

Published electronically:
October 27, 1999

MathSciNet review:
1646306

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a continuous function with and . If is convex, then , , is the characteristic function of an absolutely continuous probability distribution. The criterion complements Pólya's theorem and applies to characteristic functions with various types of behavior at the origin. In particular, it provides upper bounds on Kuttner's function , , which gives the minimal value of such that is a characteristic function. Specifically, . Furthermore, improved lower bounds on Kuttner's function are obtained from an inequality due to Boas and Kac.

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Additional Information

**Tilmann Gneiting**

Affiliation:
Department of Statistics, Box 354322, University of Washington, Seattle, Washington 98195

Email:
tilmann@stat.washington.edu

DOI:
https://doi.org/10.1090/S0002-9939-99-05200-4

Received by editor(s):
July 13, 1998

Published electronically:
October 27, 1999

Communicated by:
Christopher D. Sogge

Article copyright:
© Copyright 2000
American Mathematical Society