Sharp estimates for eigenvalues of integral operators generated by dot product kernels on the sphere

Autor(es)

Azevedo, D. ^[1] ; Menegatto, V. A. ^[2]

Afiliação do(s) autor(es)

^[1] UFJF, Dept Econ, BR-35010177 Governador Valadares, MG - Brazil

^[2] Univ Sao Paulo, ICMC, BR-13560970 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Approximation Theory; v. 177, p. 57-68, JAN 2014.
• Citações Web of Science: 2

Resumo

We obtain explicit formulas for the eigenvalues of integral operators generated by continuous dot.product kernels defined on the sphere via the usual gamma function. Using them, we present both, a procedure to describe sharp bounds for the eigenvalues and their asymptotic behavior near 0. We illustrate our results with examples, among them the integral operator generated by a Gaussian kernel. Finally, we sketch complex versions of our results to cover the cases when the sphere sits in a Hermitian space. (c) 2013 Elsevier Inc. All rights reserved. (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