Strictly positive definite functions on the unit circle

Author:
Xingping Sun

Journal:
Math. Comp. **74** (2005), 709-721

MSC (2000):
Primary 41A05, 42A15; Secondary 33C45, 33C55

Published electronically:
May 11, 2004

MathSciNet review:
2114644

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Abstract | References | Similar Articles | Additional Information

Abstract: We study strictly positive definite functions on the unit circle in the Euclidean space of dimension two. We develop several conditions pertaining to the determination of such functions. The major result is obtained by considering the set of real numbers as a vector space over the field of rational numbers and then applying the Kronecker approximation theorem and Weyl's criterion on equidistributions.

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Additional Information

**Xingping Sun**

Affiliation:
Department of Mathematics, Southwest Missouri State University, Springfield, Missouri 65804

Email:
xis280f@smsu.edu

DOI:
https://doi.org/10.1090/S0025-5718-04-01668-0

Keywords:
Strict positive-definiteness,
the Kronecker approximation,
Weyl's criterion,
equidistribution

Received by editor(s):
December 9, 2002

Received by editor(s) in revised form:
September 29, 2003

Published electronically:
May 11, 2004

Article copyright:
© Copyright 2004
American Mathematical Society