On the nuclearity of integral operators

Autor(es)

Ferreira, Jose C. ^[1] ; Menegatto, Valdir A. ^[1] ; Oliveira, Claudemir P. ^[2]

Afiliação do(s) autor(es)

^[1] ICMC USP Sao Carlos, Dept Matemat, BR-13560970 Sao Carlos, SP - Brazil

^[2] Univ Fed Itajuba, ICE DMC, BR-37500903 Itajuba, MG - Brazil

• Tipo de documento: Artigo Científico
• Fonte: POSITIVITY; v. 13, n. 3, p. 519-541, AUG 2009.
• Citações Web of Science: 14

Resumo

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)

• Processo FAPESP: 05/56694-4 - Positividade definida e a Transformada de Fourier em R^M
• Beneficiário: José Claudinei Ferreira
• Modalidade de apoio: Bolsas no Brasil - Mestrado