EIGENVALUE DECAY OF INTEGRAL OPERATORS GENERATED BY POWER SERIES-LIKE KERNELS

Autor(es)

Azevedo, D. ^[1] ; Menegatto, V. A. ^[1]

Afiliação do(s) autor(es)

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

• Tipo de documento: Artigo Científico
• Fonte: Mathematical Inequalities & Applications; v. 17, n. 2, p. 693-705, APR 2014.
• Citações Web of Science: 3

Resumo

We deduce decay rates for eigenvalues of integral operators generated by power serieslike kernels on a subset X of either R-q or C-q. A power series- like kernel is a Mercer kernel having a series expansion based on an orthogonal family [f(alpha)](alpha is an element of Z+)(q) in L-2( X, mu), in which mu is a complete measure on X. As so, we show that the eigenvalues of the integral operators are given by an explicit formula defined by the coefficients in the series expansion of the kernel and the elements of the orthogonal family. The inequalities and, in particular, the decay rates for the sequence of eigenvalues are obtained from decay assumptions on the sequence of coefficients in the expansion of the kernel and on the sequence [parallel to f(alpha)parallel to](alpha is an element of Z+)(q). (AU)

• Processo FAPESP: 10/00478-0 - Decaimento dos autovalores de operadores integrais positivos sobre a esfera.
• Beneficiário: Douglas Azevedo Sant 'Anna
• Modalidade de apoio: Bolsas no Brasil - Doutorado
• Processo FAPESP: 10/19734-6 - Análise de operadores integrais gerados por núcleos positivos definidos
• Beneficiário: Valdir Antonio Menegatto
• Modalidade de apoio: Auxílio à Pesquisa - Regular