| Full text | |
| Author(s): |
Total Authors: 2
|
| Affiliation: | [1] ICMC USP Sao Carlos, BR-13560970 Sao Carlos, SP - Brazil
Total Affiliations: 1
|
| Document type: | Journal article |
| Source: | Mathematical Inequalities & Applications; v. 17, n. 2, p. 693-705, APR 2014. |
| Web of Science Citations: | 3 |
| Abstract | |
We deduce decay rates for eigenvalues of integral operators generated by power serieslike kernels on a subset X of either R-q or C-q. A power series- like kernel is a Mercer kernel having a series expansion based on an orthogonal family [f(alpha)](alpha is an element of Z+)(q) in L-2( X, mu), in which mu is a complete measure on X. As so, we show that the eigenvalues of the integral operators are given by an explicit formula defined by the coefficients in the series expansion of the kernel and the elements of the orthogonal family. The inequalities and, in particular, the decay rates for the sequence of eigenvalues are obtained from decay assumptions on the sequence of coefficients in the expansion of the kernel and on the sequence [parallel to f(alpha)parallel to](alpha is an element of Z+)(q). (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 |