Strictly positive definite functions on the unit circle

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.

Department(s)

Mathematics

Document Type

Article

DOI

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

Keywords

Equidistribution, Strict positive-definiteness, The kronecker approximation, Weyl's criterion

Publication Date

4-1-2005

Journal Title

Mathematics of Computation

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