## A General Hilbert Space Approach to Wavelets and Its Application in Geopotential Determination

• A general approach to wavelets is presented within a framework of a separable functional Hilbert space H. Basic tool is the construction of H-product kernels by use of Fourier analysis with respect to an orthonormal basis in H. Scaling function and wavelet are defined in terms of H-product kernels. Wavelets are shown to be 'building blocks' that decorrelate the data. A pyramid scheme provides fast computation. Finally, the determination of the earth's gravitational potential from single and multipole expressions is organized as an example of wavelet approximation in Hilbert space structure.

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Author: Willi Freeden, Oliver Glockner, Rolf Litzenberger urn:nbn:de:hbz:386-kluedo-6151 Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (207) Preprint English 1999 1999 Technische Universität Kaiserslautern 2000/04/03 Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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