## Fast Wavelet Transform by Biorthogonal Locally Supported Radial Basis Functions on Fixed Spherical Grids

• 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.

Author: Ali A. Moghiseh urn:nbn:de:hbz:386-kluedo-21642 W. Freeden Doctoral Thesis English 2007 2007 Technische Universität Kaiserslautern Technische Universität Kaiserslautern 2007/12/21 2008/02/25 Biorthogonalisation ; Locally Supported Zonal Kernels ; Multiresolution Analysis; Radial Basis Functions ; Spherical Fast Wavelet Transform Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik 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 / 41A30 Approximation by other special function classes 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 / 41A58 Series expansions (e.g. Taylor, Lidstone series, but not Fourier series) 44-XX INTEGRAL TRANSFORMS, OPERATIONAL CALCULUS (For fractional derivatives and integrals, see 26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. For numerical methods, see 65R10) / 44Axx Integral transforms, operational calculus / 44A35 Convolution 45-XX INTEGRAL EQUATIONS / 45Exx Singular integral equations [See also 30E20, 30E25, 44A15, 44A35] / 45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) [See also 47B35] 65-XX NUMERICAL ANALYSIS / 65Dxx Numerical approximation and computational geometry (primarily algorithms) (For theory, see 41-XX and 68Uxx) / 65D15 Algorithms for functional approximation 65-XX NUMERICAL ANALYSIS / 65Txx Numerical methods in Fourier analysis / 65T60 Wavelets 86-XX GEOPHYSICS [See also 76U05, 76V05] / 86Axx Geophysics [See also 76U05, 76V05] / 86A04 General Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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