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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: http://dx.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