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Tue, 08 Feb 2011 12:16:54 +0100Tue, 08 Feb 2011 12:16:54 +0100Locally Supported Wavelets for the Separation of Spherical Vector Fields with Respect to their Sources
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2284
We provide a space domain oriented separation of magnetic fields into parts generated by sources in the exterior and sources in the interior of a given sphere. The separation itself is well-known in geomagnetic modeling, usually in terms of a spherical harmonic analysis or a wavelet analysis that is spherical harmonic based. However, it can also be regarded as a modification of the Helmholtz decomposition for which we derive integral representations with explicitly known convolution kernels. Regularizing these singular kernels allows a multiscale representation of the magnetic field with locally supported wavelets. This representation is applied to a set of CHAMP data for crustal field modeling.Christian Gerhardsreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2284Tue, 08 Feb 2011 12:16:54 +0100Fast Wavelet Transform by Biorthogonal Locally Supported Radial Basis Functions on Fixed Spherical Grids
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1932
The thesis is concerned with multiscale approximation by means of radial basis functions on hierarchically structured spherical grids. A new approach is proposed to construct a biorthogonal system of locally supported zonal functions. By use of this biorthogonal system of locally supported zonal functions, a spherical fast wavelet transform (SFWT) is established. Finally, based on the wavelet analysis, geophysically and geodetically relevant problems involving rotation-invariant pseudodifferential operators are shown to be efficiently and economically solvable.Ali A. Moghisehdoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1932Mon, 25 Feb 2008 10:55:30 +0100Locally Supported Approximate Identities on the Unit Ball
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1837
We present a constructive theory for locally supported approximate identities on the unit ball in \(\mathbb{R}^3\). The uniform convergence of the convolutions of the derived kernels with an arbitrary continuous function \(f\) to \(f\), i.e. the defining property of an approximate identity, is proved. Moreover, an explicit representation for a class of such kernels is given. The original publication is available at www.springerlink.comMuhammad Akram; Volker Michelpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1837Sun, 11 Feb 2007 15:03:29 +0100