| Full text | |
| Author(s): |
Total Authors: 3
|
| Affiliation: | [1] Univ Fed Uberlandia, Fac Matemat, BR-38400902 Uberlandia, MG - Brazil
[2] ICMC USP Sao Carlos, Dept Matemat, BR-13560970 Sao Carlos, SP - Brazil
Total Affiliations: 2
|
| Document type: | Journal article |
| Source: | Colloquium Mathematicum; v. 126, n. 1, p. 125-138, 2012. |
| Web of Science Citations: | 5 |
| Abstract | |
We analyze some aspects of Mercer's theory when the integral operators act on L-2(X, sigma), where X is a first countable topological space and sigma is a non-degenerate measure. We obtain results akin to the well-known Mercer's theorem and, under a positive definiteness assumption on the generating kernel of the operator, we also deduce series representations for the kernel, traceability of the operator and an integration formula to compute the trace. In this way, we upgrade considerably similar results found in the literature, in which X is always metrizable and compact and the measure sigma is finite. (AU) | |
| FAPESP's process: | 10/19734-6 - Analysis of integral operators generated by positive definite kernels |
| Grantee: | Valdir Antonio Menegatto |
| Support Opportunities: | Regular Research Grants |