Integral operators generated by Mercer-like kernels on topological spaces

M. H. Castro, V. A. Menegatto, and A. P. Peron. "Integral operators generated by Mercer-like kernels on topological spaces." Colloquium Mathematicae 126.1 (2012): 125-138. <http://eudml.org/doc/283904>.

@article{M2012,
abstract = {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.},
author = {M. H. Castro, V. A. Menegatto, A. P. Peron},
journal = {Colloquium Mathematicae},
keywords = {Mercer's theorem; integral operators; positive definite kernels; series representations; trace-class},
language = {eng},
number = {1},
pages = {125-138},
title = {Integral operators generated by Mercer-like kernels on topological spaces},
url = {http://eudml.org/doc/283904},
volume = {126},
year = {2012},
}

TY - JOUR
AU - M. H. Castro
AU - V. A. Menegatto
AU - A. P. Peron
TI - Integral operators generated by Mercer-like kernels on topological spaces
JO - Colloquium Mathematicae
PY - 2012
VL - 126
IS - 1
SP - 125
EP - 138
AB - 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.
LA - eng
KW - Mercer's theorem; integral operators; positive definite kernels; series representations; trace-class
UR - http://eudml.org/doc/283904
ER -