| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [1] Univ Tecn Federico Santa Maria, Dept Math, Av Espana 1680, Valparaiso 2390123 - Chile
[2] Univ Copenhagen, Dept Math Sci, Univ Pk 5, DK-2100 Copenhagen - Denmark
[3] Newcastle Univ, Sch Math & Stat, Newcastle Upon Tyne, Tyne & Wear - England
Total Affiliations: 3
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| Document type: | Journal article |
| Source: | Journal of Approximation Theory; v. 228, p. 58-78, APR 2018. |
| Web of Science Citations: | 6 |
| Abstract | |
Schoenberg's theorem for the complex Hilbert sphere proved by Christensen and Ressel in 1982 by Choquet theory is extended to the following result: Let L denote a locally compact group and let ID) denote the closed unit disc in the complex plane. Continuous functions f : (D) over bar x L -> C such that f (xi . eta, u(-1) v) is a positive definite kernel on the product of the unit sphere in l(2)(C) and L are characterized as the functions with a uniformly convergent expansion f(z, u) = Sigma(m,n=0) (infinity) phi(m,n)(u)z(m-n)z, where phi(m,n) is a double sequence of continuous positive definite functions on L such that Sigma phi(m,n)(e(L)) < infinity (e(L) is the neutral element of L). It is shown how the coefficient functions phi(m,n) are obtained as limits from expansions for positive definite functions on finite dimensional complex spheres via a Rodrigues formula for disc polynomials. Similar results are obtained for the real Hilbert sphere. (C) 2018 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 16/03015-7 - Positive definite functions |
| Grantee: | Ana Paula Peron |
| Support Opportunities: | Scholarships abroad - Research |
| FAPESP's process: | 14/25796-5 - (Strict) positive definite functions and differentiability |
| Grantee: | Ana Paula Peron |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 16/09906-0 - Harmonic analysis, approximation theory and applications |
| Grantee: | Dimitar Kolev Dimitrov |
| Support Opportunities: | Research Projects - Thematic Grants |