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| Author(s): |
Jose Claudinei Ferreira
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | São Carlos. |
| Institution: | Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) |
| Defense date: | 2008-02-11 |
| Examining board members: |
Valdir Antonio Menegatto;
Jorge Tulio Mujica Ascui;
Cesar Rogerio de Oliveira
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| Advisor: | Valdir Antonio Menegatto |
| Abstract | |
Firstly, we study some classical results from the theory of positive definite kernels along with some related results. Secondly, we focus on generalizations of Mercer\'s theorem and some of their implications. Special attention is given to the cases where the domain of the kernel is not compact, once the other cases are considered consistently in the literature. We include a characterization for the Fourier transform of a positive definite kernel on Rm£Rm, m ¸ 1. Finally, we apply the previous study in the analysis of decay rates for eigenvalues of integral operators generated by positive definite kernels (AU) | |