JACKSON KERNELS: A TOOL FOR ANALYSING THE DECAY OF EIGENVALUE SEQUENCES OF INTEGRAL OPERATORS ON THE SPHERE

Autor(es)

Jordao, T. ^[1] ; Menegatto, V. A. ^[1]

Afiliação do(s) autor(es)

^[1] ICMC USP Sao Carlos, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Mathematical Inequalities & Applications; v. 18, n. 4, p. 1483-1500, OCT 2015.
• Citações Web of Science: 1

Resumo

Decay rates for the sequence of eigenvalues of positive and compact integral operators have been largely investigated for a long time in the literature. In this paper, the focus will be on positive integral operators acting on square integrable functions on the unit sphere and generated by a kernel satisfying a Holder type assumption defined by average operators. In the approach to be presented here, the decay rate will be reached from convenient estimations on the eigenvalues of the operator themselves, with the help of specific properties of a generic approximation operator defined through the so-called generalized Jackson kernels. The decay rate has the same structure of those known to hold in the cases in which the Holder condition is the classical one. Therefore, within the spherical setting, the abstract approach to be introduced here extends some classical results on the topic. (AU)

• Processo FAPESP: 14/06209-1 - Coeficientes de Fourier, K-funcionais e aplicações
• Beneficiário: Thaís Jordão
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 14/00277-5 - Núcleos positivos definidos e operadores integrais associados
• Beneficiário: Valdir Antonio Menegatto
• Modalidade de apoio: Auxílio à Pesquisa - Regular