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Doctoral Thesis
DOI
https://doi.org/10.11606/T.55.2019.tde-10062019-145848
Document
Author
Full name
Jean Carlo Guella
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2019
Supervisor
Committee
Menegatto, Valdir Antonio (President)
Dimitrov, Dimitar Kolev
Jordão, Thaís
Tozoni, Sergio Antonio
Title in English
A unifying approach to isotropic and radial positive definite kernels
Keywords in English
Conditionally negative definite kernels
Isotropic kernel on spheres
Positive definite kernels
Radial kernels on Euclidean spaces
Strictly positive definite kernels
Abstract in English
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.
Title in Portuguese
Um estudo uniforme para núcleos positivos definidos radiais e isotrópicos
Keywords in Portuguese
Núcleos condicionalmente negativos definidos
Núcleos estritamente positivos definidos
Núcleos isotrópicos em esferas
Núcleos Radiais em espaços Euclidianos, Núcleos positivos definidos
Abstract in Portuguese
Neste trabalho, nós generalizamos três resultados famosos obtidos por Schoenberg: I) a caracterização dos núcleos contínuos isotrópicos positivos definidos em esferas reais; II) a caracterização dos núcleos contínuos radiais positivos definidos em espaços Euclidianos; III) a caracterização dos núcleos contínuos radiais condicionalmente negativos definidos em espaços Euclidianos. A partir destas novas abordagens, reobtemos vários resultados da literatura assim como obtemos novos. Com a exceção de S1 e R, obtemos condições necessárias e suficientes para que estes núcleos sejam estritamente positivos definidos e estritamente condicionalmente negativos definidos.
 
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Publishing Date
2019-06-10
 
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