2012
DOI: 10.1080/01630563.2012.660590
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Reproducing Properties of Differentiable Mercer-Like Kernels on the Sphere

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Cited by 11 publications
(4 citation statements)
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“… . If (11) holds, then by Theorem 2.4 in [31], or Theorem 4.2 in [32] or Proposition 6.2 in [33] that:…”
Section: { }mentioning
confidence: 99%
“… . If (11) holds, then by Theorem 2.4 in [31], or Theorem 4.2 in [32] or Proposition 6.2 in [33] that:…”
Section: { }mentioning
confidence: 99%
“…It is expected that the functions in a RKHS inherit some of the properties of the generating kernel such as smoothness. In [13] the authors showed that functions in the RKHS associated to a kernel having a Mercer series expansion (it means a Fourier-like series given in terms of tensorial product of orthonormal functions) have the same "degree" of smoothness in terms of the fractional Laplace-Beltrami derivative of the original kernel. More general than that, in [12] similar harmonic analysis structure was enough to prove similar reproducing results on a very general context.…”
Section: Introductionmentioning
confidence: 99%
“…No capítulo anterior (veja também [13]), assumindo certas hipóteses de diferenciabilidade sobre um núcleo de Mercer K deduzimos propriedades de diferenciabilidade para funções de H K . Dentre as muitas noções de diferenciabilidade para funções definidas na esfera S m , a diferenciabilidade usual foi a escolhida.…”
Section: Séries De Fourier-laplace Com Pesos Em Ehrunclassified