EIGENVALUE DECAY OF POSITIVE INTEGRAL OPERATORS ON THE SPHERE

Autor(es)

Castro, M. H. ^[1] ; Menegatto, V. A. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Fed Uberlandia, Fac Matemat, BR-38400902 Uberlandia, MG - Brazil

^[2] ICMC USP, Dept Matemat, BR-13560970 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Mathematics of Computation; v. 81, n. 280, p. 2303-2317, OCT 2012.
• Citações Web of Science: 9

Resumo

We obtain decay rates for singular values and eigenvalues of integral operators generated by square integrable kernels on the unit sphere in Rm+1, m >= 2, under assumptions on both, certain derivatives of the kernel and the integral operators generated by such derivatives. This type of problem is common in the literature but the assumptions are usually defined using standard differentiation in It Rm+1. In this paper, the assumptions are all defined via the Laplace-Beltrami derivative, a concept first investigated by Rudin in the early fifties and genuinely spherical in nature. The rates we present depend on both, the differentiability order used to define the smoothness conditions and the dimension m. They are shown to be optimal. (AU)

• 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