| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] ICMC USP Sao Carlos, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil
Total Affiliations: 1
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| Document type: | Journal article |
| Source: | Mathematical Inequalities & Applications; v. 18, n. 4, p. 1483-1500, OCT 2015. |
| Web of Science Citations: | 1 |
| Abstract | |
Decay rates for the sequence of eigenvalues of positive and compact integral operators have been largely investigated for a long time in the literature. In this paper, the focus will be on positive integral operators acting on square integrable functions on the unit sphere and generated by a kernel satisfying a Holder type assumption defined by average operators. In the approach to be presented here, the decay rate will be reached from convenient estimations on the eigenvalues of the operator themselves, with the help of specific properties of a generic approximation operator defined through the so-called generalized Jackson kernels. The decay rate has the same structure of those known to hold in the cases in which the Holder condition is the classical one. Therefore, within the spherical setting, the abstract approach to be introduced here extends some classical results on the topic. (AU) | |
| FAPESP's process: | 14/06209-1 - Fourier coefficients, K-functionals and applications |
| Grantee: | Thaís Jordão |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 14/00277-5 - Positive definite kernels and integral operators generated by them |
| Grantee: | Valdir Antonio Menegatto |
| Support Opportunities: | Regular Research Grants |