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A method for fast evaluation of band-limited functions (spherical polynomials) at many scattered points on the unit 2-d sphere is presented. The method relies on the superb localization of the father needlet kernels and their compatibility with spherical harmonics. It is fast, local, memory efficient, numerically stable and with guaranteed (prescribed)… (More)

We present a characterization of the approximation errors of the Post-Widder and the Gamma operators in Lp(0, ∞), 1 ≤ p ≤ ∞, with a weight x γ for any real γ. Two types of characteristics are used – weighted K-functionals of the approximated function itself and the classical fixed step moduli of smoothness taken on a simple modification of it.

An algorithm for fast and accurate evaluation of band-limited functions at many scattered points on the unit 2-d sphere is developed. The algorithm is based on trigonometric representation of spherical harmonics in spherical coordinates and highly localized tensor-product trigonometric kernels (needlets). It is simple, fast, local, memory efficient,… (More)

We present a characterization of the approximation errors of the Post-Widder and the Gamma operators in Lp(0, ∞), 1 ≤ p ≤ ∞, with a weight x γ 0 (1 + x) γ∞−γ 0 with arbitrary real γ0, γ∞. Two types of characteristics are used – weighted K-functionals of the approximated function itself and the classical fixed step moduli of smoothness taken on simple… (More)

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