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Master's Dissertation
DOI
10.11606/D.55.2018.tde-06042018-170037
Document
Author
Full name
Ana Paula Peron
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 1995
Supervisor
Committee
Menegatto, Valdir Antonio (President)
Andrade, Eliana Xavier Linhares de
Dias, Ires
Title in Portuguese
Interpolação no Círculo Usando Funções Condicionalmente Negativas e Definidas
Keywords in Portuguese
Não disponível
Abstract in Portuguese
Estudamos, sistematicamente, funções condicionalmente negativas definidas sobre o círculo. Quando tais funções são também estritamente condicionalmente negativas definidas, então elas podem ser utilizadas em soluções de certos problemas de interpolação de dados arbitrários sobre pontos do círculo. Condições necessárias e condições suficientes para condicionalidade estrita negativa definida são apresentadas. A utilização de funções condicionalmente negativas definidas para interpolar dados sobre um subconjunto do círculo que não contém pares de pontos antipodais é então estudada. O caso particular em que a função coincide com a identidade é analisado sob essa perspectiva.
Title in English
Interpolation on the circle via conditionally negative definite functions
Keywords in English
Not available
Abstract in English
We systematically study conditionally negative definite functions on the circle. When such functions are, in addition, strictly conditionally negative definite, then they can be employed to generate solutions of certain interpolation problerns to arbitrary data on the circle. Separated necessary and sufficient conditions for strict conditional negative definiteness are presented. The possible use of conditionally negative definite functions to interpolate arbitrary data on a subset of the circle, not containing pairs of antipodal points, is studied. Finally, the particular case when the function is the identity itself is analysed.
 
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AnaPaulaPeron.pdf (29.56 Mbytes)
Publishing Date
2018-04-06
 
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