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

Autor(es)

Guella, J. C. ^[1] ; Menegatto, V. A. ^[1]

Afiliação do(s) autor(es)

^[1] ICMC USP, Dept Matemat, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS; v. 25, n. 4, p. 1424-1446, AUG 2019.
• Citações Web of Science: 1

Resumo

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)

• Processo FAPESP: 16/09906-0 - Análise harmônica, teoria da aproximação, funções especiais e aplicações
• Beneficiário: Dimitar Kolev Dimitrov
• Modalidade de apoio: Auxílio à Pesquisa - Temático