منابع مشابه
Filtered polynomial approximation on the sphere
Localised polynomial approximations on the sphere have a variety of applications in areas such as signal processing, geomathematics and cosmology. Filtering is a simple and effective way of constructing a localised polynomial approximation. In this thesis we investigate the localisation properties of filtered polynomial approximations on the sphere. Using filtered polynomial kernels and a speci...
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A fully implementable filtered polynomial approximation on spherical shells is considered. The method proposed is a quadrature-based version of a filtered polynomial approximation. The radial direction and the angular direction of the shells are treated separately with constructive filtered polynomial approximation. The approximation error with respect to the supremum norm is shown to decay alg...
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We consider the problem of approximately reconstructing a function f defined on the surface of the unit sphere in the Euclidean space R, using samples of f at scattered sites. A central role is played by the construction of a new operator for polynomial approximation, which is a uniformly bounded quasi–projection in the de la Vallée Poussin style, i.e. it reproduces spherical polynomials up to ...
متن کاملSpherical Designs and Polynomial Approximation on the Sphere
This talk presents some joint work with An, Frommer, Lang, Sloan and Womersley on spherical designs and polynomial approximation on the sphere [1],[2],[4],[5]. Finding “good” finite sets of points on the unit sphere S in the Euclidean space R has been a hot research topic in mathematics, physics, and engineering for more than hundred years. There are several concepts of “good” finite sets of po...
متن کاملPolynomial frames on the sphere
We introduce a class of polynomial frames suitable for analyzing data on the surface of the unit sphere of a Euclidean space. Our frames consist of polynomials, but are well localized, and are stable with respect to all the Lp norms. The frames belonging to higher and higher scale wavelet spaces have more and more vanishing moments. 1 ∗The research of this author was supported, in part, by gran...
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ژورنال
عنوان ژورنال: Journal of Fourier Analysis and Applications
سال: 2016
ISSN: 1069-5869,1531-5851
DOI: 10.1007/s00041-016-9493-7