Integral operators generated by Mercer-like kernels on topological spaces

• Autorzy: M. H. Castro , V. A. Menegatto , A. P. Peron
• Języki publikacji: EN

Abstrakty

EN

We analyze some aspects of Mercer's theory when the integral operators act on L²(X,σ), where X is a first countable topological space and σ 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 σ is finite.

Kategorie tematyczne

• 45P05: Integral operators
• 42A82: Positive definite functions
• 47G10: Integral operators
• 45H05: Miscellaneous special kernels
• 47B34: Kernel operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2012
• Tom: 126
• Numer: 1
• Strony: 125-138

Daty

wydano

2012

Twórcy

autor

M. H. Castro

• Faculdade de Matemática, Universidade Federal de Uberlândia, Caixa Postal 593, 38400-902 Uberlândia MG, Brasil

autor

V. A. Menegatto

• Departamento de Matemática, ICMC-USP - São Carlos, Caixa Postal 668, 13560-970 São Carlos SP, Brasil

autor

A. P. Peron

• Departamento de Matemática, ICMC-USP - São Carlos, Caixa Postal 668, 13560-970 São Carlos SP, Brasil

Identyfikatory

DOI

10.4064/cm126-1-9