Strictly positive definite functions on the unit circle

Sun, Xingping

doi:10.1090/S0025-5718-04-01668-0

Strictly positive definite functions on the unit circle
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Math. Comp. 74 (2005), 709-721 Request permission

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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