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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Schoenberg's Theorem for Positive Definite Functions on Products: A Unifying Framework

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Author(s):
Guella, J. C. [1] ; Menegatto, V. A. [1]
Total Authors: 2
Affiliation:
[1] ICMC USP, Dept Matemat, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil
Total Affiliations: 1
Document type: Journal article
Source: JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS; v. 25, n. 4, p. 1424-1446, AUG 2019.
Web of Science Citations: 1
Abstract

The main contribution in the present paper is a characterization for positive definiteness and strict positive definiteness of a kernel on the product XxSd, in which X is a nonempty set and Sd is the usual d-dimensional unit sphere in Euclidean space, through Fourier-like expansions. The setting presupposes continuity and isotropy on the Sd side and no algebraic structure or topology on X. The result may be interpreted as another extension of a classical result of I. J. Schoenberg on positive definite functions on spheres. We take a closer look at our results in the case in which X is a locally compact group, paying special attention to usual Euclidean spaces and high dimensional tori. (AU)

FAPESP's process: 16/09906-0 - Harmonic analysis, approximation theory and applications
Grantee:Dimitar Kolev Dimitrov
Support Opportunities: Research Projects - Thematic Grants