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Strictly positive definite functions on the unit circle
Author(s):
Xingping
Sun.
Journal:
Math. Comp.
74
(2005),
709-721.
MSC (2000):
Primary 41A05, 42A15;
Secondary 33C45, 33C55
Posted:
May 11, 2004
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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.
References:
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Additional Information:
Xingping
Sun
Affiliation:
Department of Mathematics, Southwest Missouri State University, Springfield, Missouri 65804
Email:
xis280f@smsu.edu
DOI:
10.1090/S0025-5718-04-01668-0
PII:
S 0025-5718(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
Posted:
May 11, 2004
Copyright of article:
Copyright
2004,
American Mathematical Society
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