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Mathematics > Classical Analysis and ODEs

Title: Characterization of Strict Positive Definiteness on products of complex spheres

Abstract: In this paper we consider Positive Definite functions on products $\Omega_{2q}\times\Omega_{2p}$ of complex spheres, and we obtain a condition, in terms of the coefficients in their disc polynomial expansions, which is necessary and sufficient for the function to be Strictly Positive Definite. The result includes also the more delicate cases in which $p$ and/or $q$ can be $1$ or $\infty$.
The condition we obtain states that a suitable set in $\mathbb{Z}^2$, containing the indexes of the strictly positive coefficients in the expansion, must intersect every product of arithmetic progressions.
Subjects: Classical Analysis and ODEs (math.CA)
MSC classes: 42A82, 42C10
Cite as: arXiv:1803.06264 [math.CA]
  (or arXiv:1803.06264v1 [math.CA] for this version)

Submission history

From: Ana P. Peron [view email]
[v1] Fri, 16 Mar 2018 15:16:42 GMT (22kb)