Weighted Fourier-Laplace transforms in reproducing kernel Hilbert spaces on the sphere

Autor(es)

Jordao, T. ^[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: Journal of Mathematical Analysis and Applications; v. 411, n. 2, p. 732-741, MAR 15 2014.
• Citações Web of Science: 6

Resumo

We study the action of a weighted Fourier-Laplace transform on the functions in the reproducing kernel Hilbert space (RKHS) associated with a positive definite kernel on the sphere. After defining a notion of smoothness implied by the transform, we show that smoothness of the kernel implies the same smoothness for the generating elements (spherical harmonics) in the Mercer expansion of the kernel. We prove a reproducing property for the weighted Fourier-Laplace transform of the functions in the RKHS and embed the RKHS into spaces of smooth functions. Some relevant properties of the embedding are considered, including compactness and boundedness. The approach taken in the paper includes two important notions of differentiability characterized by weighted Fourier-Laplace transforms: fractional derivatives and Laplace-Beltrami derivatives. (C) 2013 Elsevier Inc. All rights reserved. (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
• Processo FAPESP: 08/57085-0 - Espacos nativos associados a nucleo de mercer suaves sobre a esfera
• Beneficiário: Thaís Jordão
• Modalidade de apoio: Bolsas no Brasil - Doutorado