Strictly positive definite functions on the unit circle
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.
Equidistribution, Strict positive-definiteness, The kronecker approximation, Weyl's criterion
Sun, Xingping. "Strictly positive definite functions on the unit circle." Mathematics of Computation 74, no. 250 (2005): 709-721.
Mathematics of Computation