A unifying approach to isotropic and radial positive definite kernels

• Autor(a) principal: Guella, Jean Carlo
• Data de Publicação: 2019
• Tipo de documento: Tese
• Idioma: eng
• Título da fonte: Biblioteca Digital de Teses e Dissertações da USP
• Texto Completo: http://www.teses.usp.br/teses/disponiveis/55/55135/tde-10062019-145848/
• topic: Conditionally negative definite kernels; Isotropic kernel on spheres; Núcleos condicionalmente negativos definidos; Núcleos estritamente positivos definidos; Núcleos isotrópicos em esferas; Núcleos Radiais em espaços Euclidianos, Núcleos positivos definidos; Positive definite kernels; Radial kernels on Euclidean spaces; Strictly positive definite kernels

In this work, we generalize three famous results obtained by Schoenberg: I) the characterization of the continuous positive definite isotropic kernels defined on a real sphere; II) the characterization of the continuous positive definite radial kernels defined on an Euclidean space; III) the characterization of the continuous conditionally negative radial kernels defined on an Euclidean space. From this new approach, we reobtain several results in the literature and obtain some new ones as well. With the exception of S1 and R , we obtain necessary and sufficient conditions in order that these kernels be strictly positive definite and strictly conditionally negative definite.