A LIMIT FORMULA FOR SEMIGROUPS DEFINED BY FOURIER-JACOBI SERIES

Autor(es)

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

Afiliação do(s) autor(es)

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

• Tipo de documento: Artigo Científico
• Fonte: Proceedings of the American Mathematical Society; v. 146, n. 5, p. 2027-2038, MAY 2018.
• Citações Web of Science: 1

Resumo

I. J. Schoenberg showed the following result in his celebrated paper {[}Schoenberg, I. J., Positive definite functions on spheres. Duke Math. J. 9 (1942), 96-108]: let center dot and S-d denote the usual inner product and the unit sphere in Rd+1, respectively. If F-d stands for the class of real continuous functions f with domain {[}-1, 1] defining positive definite kernels (x, y) is an element of S-d x S-d -> f(x center dot y), then the class boolean AND(d >= 1) F-d coincides with the class of probability generating functions on {[}-1, 1]. In this paper, we present an extension of this result to classes of continuous functions defined by Fourier-Jacobi expansions with nonnegative coefficients. In particular, we establish a version of the above result in the case in which the spheres Sd are replaced with compact two-point homogeneous spaces. (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