Wavelets, Multiscale Systems and Hypercomplex Analysis

Cover -- TOC36;Contents -- Editorial Introduction -- CH36;Teodorescu Transform Decomposition of Multivector Fields on Fractal Hypersurfaces -- 146; Introduction -- 246; Preliminaries -- 246;146; Clifford algebras and multivectors -- 246;246; Clifford analysis and harmonic multivector fields -- 246;346; Fractal dimensions and Whitney extension theorem -- 346; Jump problem and monogenic extensions -- 446; K45;Multivectorial case46; Dynkin problem and harmonic extension -- 546; Example -- 546;146; The curve of B46; Kats -- 546;246; The surface G[Sub40;42;41;] -- 546;346; The function u[Sub40;42;41;] -- 546;446; Proof of properties a41; 183; 183; 183; e41; -- References -- CH36;Metric Dependent Clifford Analysis with Applications to Wavelet Analysis -- 146; Introduction -- 246; The metric dependent Clifford toolbox -- 246;146; Tensors -- 246;246; From Grassmann to Clifford -- 246;346; Embeddings of R[Sup40;m41;] -- 246;446; Fischer duality and Fischer decomposition -- 246;546; The Euler and angular Dirac operators -- 246;646; Solid g45;spherical harmonics -- 246;746; The g45;Fourier transform -- 346; Metric invariant integration theory -- 346;146; The basic language of Clifford differential forms -- 346;246; Orthogonal spherical monogenics -- 446; The radial g45;Clifford45;Hermite polynomials and associated CCWT -- 446;146; The radial g45;Clifford45;Hermite polynomials -- 446;246; The g45;Clifford45;Hermite wavelets -- 446;346; The g45;Clifford45;Hermite Continuous Wavelet Transform -- References -- CH36;A Hierarchical Semi45;Separable Moore45;Penrose Equation Solver -- 146; Introduction -- 246; HSS representations -- 346; Preliminaries -- 446; HSS row absorption procedure -- Complexity calculation -- 546; An HSS Moore45;Penrose reduction method -- 646; Discussion and conclusions -- Acknowledgements -- References -- CH36;Methods from Multiscale Theory and Wavelets Applied to Nonlinear Dynamics -- 146; Introduction -- 246; Connection to signal processing and wavelets -- 346; Motivating examples44; nonlinearity -- MRAs in geometry and operator theory -- 346;146; Spectrum and geometry58; wavelets44; tight frames44; and Hilbert spaces on Julia sets -- 346;246; Multiresolution analysis 40;MRA41; -- 346;346; Julia sets from complex dynamics -- 446; Main results -- 446;146; Spectral decomposition of covariant representations58; projective limits -- 546; Remarks on other applications -- Acknowledgements -- References -- CH36;Noncommutative Trigonometry -- 146; Introduction -- 246; The first 40;active41; period 19668211;1972 -- 346; The second 40;intermittent41; period 19738211;1993 -- 446; The third 40;most active41; period 19948211;2005 -- 546; Related work58; Discussion -- 646; Noncommutative trigonometry58; Outlook -- 646;146; Extensions to matrix and operator algebras -- 646;246; Multiscale system theory44; wavelets44; iterative methods -- 646;346; Quantum mechanics -- References -- CH36;Stationary Random Fields.