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Mon, 07 Apr 2008 13:48:15 +0200Mon, 07 Apr 2008 13:48:15 +0200On the Completeness and Closure of Vector and Tensor Spherical Harmonics
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1943
An intrinsically on the 2-sphere formulated proof of the closure and completeness of spherical harmonics is given in vectorial and tensorial framework. The considerations are essentially based on vector and tensor approximation in terms of zonal vector and tensor Bernstein kernels, respectively.Willi Freeden; Martin Guttingpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1943Mon, 07 Apr 2008 13:48:15 +0200Easy Differentiation and Integration of Homogeneous Harmonic Polynomials
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1688
We will give explicit differentiation and integration rules for homogeneous harmonic polynomial polynomials and spherical harmonics in IR^3 with respect to the following differential operators: partial_1, partial_2, partial_3, x_3 partial_2 - x_2 partial_3, x_3 partial_1 - x_1 partial_3, x_2 partial_1 - x_1 partial_2 and x_1 partial_1 + x_2 partial_2 + x_3 partial_3. A numerical application to the problem of determining the geopotential field will be shown.Frank Bauerpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1688Fri, 02 Dec 2005 23:40:42 +0100The Spherical Bernstein Wavelet
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1637
In this work we introduce a new bandlimited spherical wavelet: The Bernstein wavelet. It possesses a couple of interesting properties. To be specific, we are able to construct bandlimited wavelets free of oscillations. The scaling function of this wavelet is investigated with regard to the spherical uncertainty principle, i.e., its localization in the space domain as well as in the momentum domain is calculated and compared to the well-known Shannon scaling function. Surprisingly, they possess the same localization in space although one is highly oscillating whereas the other one shows no oscillatory behavior. Moreover, the Bernstein scaling function turns out to be the first bandlimited scaling function known to the literature whose uncertainty product tends to the minimal value 1.Martin J. Fengler; Willi Freeden; Martin Guttingpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1637Fri, 20 May 2005 12:07:21 +0200