| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] UFJF, Dept Econ, BR-35010177 Governador Valadares, MG - Brazil
[2] Univ Sao Paulo, ICMC, BR-13560970 Sao Carlos, SP - Brazil
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | Journal of Approximation Theory; v. 177, p. 57-68, JAN 2014. |
| Web of Science Citations: | 2 |
| Abstract | |
We obtain explicit formulas for the eigenvalues of integral operators generated by continuous dot.product kernels defined on the sphere via the usual gamma function. Using them, we present both, a procedure to describe sharp bounds for the eigenvalues and their asymptotic behavior near 0. We illustrate our results with examples, among them the integral operator generated by a Gaussian kernel. Finally, we sketch complex versions of our results to cover the cases when the sphere sits in a Hermitian space. (c) 2013 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 10/00478-0 - Decay rates for eigenvalues of positive integral operators on the sphere. |
| Grantee: | Douglas Azevedo Sant 'Anna |
| Support Opportunities: | Scholarships in Brazil - Doctorate |
| FAPESP's process: | 10/19734-6 - Analysis of integral operators generated by positive definite kernels |
| Grantee: | Valdir Antonio Menegatto |
| Support Opportunities: | Regular Research Grants |