| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] ICMC USP Sao Carlos, Dept Matemat, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil
Total Affiliations: 1
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| Document type: | Journal article |
| Source: | Proceedings of the American Mathematical Society; v. 146, n. 5, p. 2027-2038, MAY 2018. |
| Web of Science Citations: | 1 |
| Abstract | |
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) | |
| FAPESP's process: | 16/09906-0 - Harmonic analysis, approximation theory and applications |
| Grantee: | Dimitar Kolev Dimitrov |
| Support Opportunities: | Research Projects - Thematic Grants |