INTEGRAL OPERATORS GENERATED BY MERCER-LIKE KERNELS ON TOPOLOGICAL SPACES

Autor(es)

Castro, M. H. ^[1] ; Menegatto, V. A. ^[2] ; Peron, A. P. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Fed Uberlandia, Fac Matemat, BR-38400902 Uberlandia, MG - Brazil

^[2] ICMC USP Sao Carlos, Dept Matemat, BR-13560970 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Colloquium Mathematicum; v. 126, n. 1, p. 125-138, 2012.
• Citações Web of Science: 5

Resumo

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)

• Processo FAPESP: 08/54221-0 - Aproximacao da identidade e nucleos positivos definidos em esferas
• Beneficiário: Ana Paula Peron
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 10/19734-6 - Análise de operadores integrais gerados por núcleos positivos definidos
• Beneficiário: Valdir Antonio Menegatto
• Modalidade de apoio: Auxílio à Pesquisa - Regular