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Master's Dissertation
DOI
10.11606/D.55.2007.tde-26042007-120351
Document
Author
Full name
Mario Henrique de Castro
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2007
Supervisor
Committee
Menegatto, Valdir Antonio (President)
Silva, Evandro Raimundo da
Tozoni, Sergio Antonio
Title in Portuguese
Diferentes noções de diferenciabilidade para funções definidas na esfera
Keywords in Portuguese
Diferenciabilidade
Esfera
Fórmula da adição
Funções homogêneas
Funk-Hecke
Harmônicos esféricos
Laplace-Beltrami
Abstract in Portuguese
Neste trabalho estudamos diferentes noções de diferenciabilidade para funções definidas na esfera unitária S^n-1 de R^n, n>=2. Em relação à derivada usual, encontramos condições necessárias e/ou suficientes para que uma função seja diferenciável até uma ordem fixada. Para as outras duas, a derivada forte de Laplace-Beltrami e a derivada fraca, apresentamos algumas propriedades básicas e procuramos condições que garantam a equivalência destas com a diferenciabilidade usual.
Title in English
Different notions of differentiability for functions defined on the sphere
Keywords in English
Addition formula
Differentiability
Funk-Hecke
Homogeneous functions
Laplace-Beltrami
sphere
Spherical harmonics
Abstract in English
In this work we study different notions of differentiability for functions defined on the unit sphere S^n-1 of R^n, n>=2. With respect to the usual derivative, we find necessary and/or sufficient conditions in order that a function be differentiable up to a fixed order. As for the other two, the strong Laplace-Beltrami derivative and the weak derivative, we present some basic properties about them and search for conditions that guarantee the equivalence of them with the previous one.
 
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dissertacaomario.pdf (632.83 Kbytes)
Publishing Date
2007-05-08
 
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