Wavelets, Multiscale Systems and Hypercomplex Analysis

From a mathematical point of view it is fascinating to realize that most, if not all, of the notions arising from the theory of analytic functions in the open unit disk have counterparts when one replaces the integers by the nodes of a homogeneous tree. It is also fascinating to realize that a whole function theory, different from the classical theory of several complex variables, can be developped when one considers hypercomplex (Clifford) variables, Fueter polynomials and the Cauchy-Kovalevskaya product, in place of the classical polynomials in three independent variables.

This volume contains a selection of papers on the topics of Clifford analysis and wavelets and multiscale analysis, the latter being understood in a very wide sense. The theory of wavelets is mathematically rich and has many practical applications.

Contributors: R. Abreu-Blaya, J. Bory-Reyes, F. Brackx, Sh. Chandrasekaran, N. de Schepper, P. Dewilde, D.E. Dutkay, K. Gustafson, H. Heyer, P.E.T. Jorgensen, T. Moreno-García, L. Peng, F. Sommen, M.W. Wong, J. Zhao, H. Zhu

Teodorescu Transform Decomposition of Multivector Fields on Fractal Hypersurfaces.- Metric Dependent Clifford Analysis with Applications to Wavelet Analysis.- A Hierarchical Semi-separable Moore-Penrose Equation Solver.- Methods from Multiscale Theory and Wavelets Applied to Nonlinear Dynamics.- Noncommutative Trigonometry.- Stationary Random Fields over Graphs and Related Structures.- Matrix Representations and Numerical Computations of Wavelet Multipliers.- Clifford Algebra-valued Admissible Wavelets Associated to More than 2-dimensional Euclidean Group with Dilations.