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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

On the nuclearity of integral operators

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Author(s):
Ferreira, Jose C. [1] ; Menegatto, Valdir A. [1] ; Oliveira, Claudemir P. [2]
Total Authors: 3
Affiliation:
[1] ICMC USP Sao Carlos, Dept Matemat, BR-13560970 Sao Carlos, SP - Brazil
[2] Univ Fed Itajuba, ICE DMC, BR-37500903 Itajuba, MG - Brazil
Total Affiliations: 2
Document type: Journal article
Source: POSITIVITY; v. 13, n. 3, p. 519-541, AUG 2009.
Web of Science Citations: 14
Abstract

Let X be a nonempty measurable subset of R(m) and consider the restriction of the usual Lebesgue measure sigma of R(m) to X. Under the assumption that the intersection of X with every open ball of R(m) has positive measure, we find necessary and sufficient conditions on a L(2)(X)-positive definite kernel K : X x X -> C in order that the associated integral operator K : L(2)(X) -> L(2)(X) be nuclear. Taken nuclearity for granted, formulas for the trace of the operator are derived. Some of the results are re-analyzed when K is just an element of L(2)(X x X). (AU)