## On the Multiscale Solution of Satellite Problems by Use of Locally Supported Kernel Functions Corresponding to Equidistributed Data on Spherical Orbits

• Being interested in (rotation-)invariant pseudodi erential equations of satellite problems corresponding to spherical orbits, we are reasonably led to generating kernels that depend only on the spherical distance, i. e. in the language of modern constructive approximation form spherical radial basis functions. In this paper approximate identities generated by such (rotation-invariant) kernels which are additionally locally supported are investigated in detail from theoretical as well as numerical point of view. So-called spherical di erence wavelets are introduced. The wavelet transforms are evaluated by the use of a numerical integration rule, that is based on Weyl's law of equidistribution. This approximate formula is constructed such that it can cope with millions of (satellite) data. The approximation error is estimated on the orbital sphere. Finally, we apply the developed theory to the problems of satellite-to-satellite tracking (SST) and satellite gravity gradiometry (SGG).

Author: Willi Freeden, Kerstin Hesse urn:nbn:de:hbz:386-kluedo-10542 Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (233) Preprint English 2000 2000 Technische Universität Kaiserslautern 2000/08/21 Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik 34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Axx General theory / 34A55 Inverse problems 41-XX APPROXIMATIONS AND EXPANSIONS (For all approximation theory in the complex domain, see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numerical approximation, see 65Dxx) / 41Axx Approximations and expansions / 41A35 Approximation by operators (in particular, by integral operators) 65-XX NUMERICAL ANALYSIS / 65Jxx Numerical analysis in abstract spaces / 65J20 Improperly posed problems; regularization Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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