Aproximação na esfera por uma soma com pesos de harmônicos esféricos / Approximation on the sphere by weighted sums of spherical harmonics

AUTOR(ES)

Ana Carla Piantella

DATA DE PUBLICAÇÃO

2007

RESUMO

The subject of this work is to study approximation on the sphere by weighted sums of spherical harmonics. We present necessary and sufficient conditions on the weights for convergence in both, the continuous and the Lp cases. We analyse the convergence rates of the approximation processes using a modulus of smoothness related to the strong Laplace- Beltrami derivative. We include proofs for several results related to such a derivative, since we were unable to find them in the literature

ASSUNTO(S)

spherical shifting aproximação módulo de suavidade esférico translação esférica esfera harmônicos esféricos spherical convolution sphere convolução esférica derivada forte de laplace-beltrami rates of convergence aproximation ordem de convergência modulus of smoothness spherical harmonics strong laplace-beltrami derivative

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