ESTIMATES FOR FOURIER SUMS AND EIGENVALUES OF INTEGRAL OPERATORS VIA MULTIPLIERS ON THE SPHERE

Autor(es)

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

Afiliação do(s) autor(es)

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

• Tipo de documento: Artigo Científico
• Fonte: Proceedings of the American Mathematical Society; v. 144, n. 1, p. 269-283, JAN 2016.
• Citações Web of Science: 2

Resumo

We provide estimates for weighted Fourier sums of integrable functions defined on the sphere when the weights originate from a multiplier operator acting on the space where the function belongs. That implies refined estimates for weighted Fourier sums of integrable kernels on the sphere that satisfy an abstract Holder condition based on a parameterized family of multiplier operators defining an approximate identity. This general estimation approach includes an important class of multiplier operators, namely, that defined by convolutions with zonal measures. The estimates are used to obtain decay rates for the eigenvalues of positive integral operators on L-2(S-m) and generated by a kernel satisfying the Holder condition based on multiplier operators on L-2(S-m). (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: 11/21300-7 - Autovalores de operadores integrais gerados por núcleos satisfazendo condições de Hölder abstratas
• Beneficiário: Thaís Jordão
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado