An extension of Mercer's theory to L-p

Autor(es)

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

Afiliação do(s) autor(es)

^[1] Univ Fed Alfenas, Alfenas, MG - Brazil

^[2] ICMC USP, Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: POSITIVITY; v. 16, n. 2, p. 197-212, JUN 2012.
• Citações Web of Science: 3

Resumo

Let X be a topological space, either locally compact or first countable, endowed with a strictly positive measure nu and kappa : L-2(X, nu) -> L-2(X, nu) an integral operator generated by a Mercer like kernel K. In this paper we extend Mercer's theory for K and kappa under the assumption that the function chi is an element of X -> K (chi, chi) belongs to some L-p/2(X, nu), p >= 1. In particular, we obtain series representations for K and some powers of kappa, with convergence in the p-mean, and show that the range of certain powers of kappa contains continuous functions only. These results are used to estimate the approximation numbers of a modified version of kappa acting on L-p (X, nu). (AU)

• Processo FAPESP: 07/58086-7 - Operadores integrais gerados por nucleos positivos definidos.
• Beneficiário: José Claudinei Ferreira
• Modalidade de apoio: Bolsas no Brasil - Doutorado