| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] ICMC USP Sao Carlos, BR-13560970 Sao Carlos, SP - Brazil
Total Affiliations: 1
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| Document type: | Journal article |
| Source: | Journal of Mathematical Analysis and Applications; v. 411, n. 2, p. 732-741, MAR 15 2014. |
| Web of Science Citations: | 6 |
| Abstract | |
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) | |
| FAPESP's process: | 10/19734-6 - Analysis of integral operators generated by positive definite kernels |
| Grantee: | Valdir Antonio Menegatto |
| Support Opportunities: | Regular Research Grants |