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Wavelets, Multiscale Systems and Hypercomplex Analysis

  • Book
  • © 2006

Overview

Editors:
  1. Daniel Alpay

    1. Department of Mathematics, Ben-Gurion University of the Negev, Beer Sheva, Israel

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  2. Annemarie Luger

    1. Institut für Analysis und Scientiific Computing, Technische Universität Wien, Wien, Austria

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  3. Harald Woracek

    1. Institut für Analysis und Scientiific Computing, Technische Universität Wien, Wien, Austria

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  • First-rate contributors, most articles have been written on invitation
  • Unique collection of material, particularly relating Clifford analysis and the theory of wavelets

Part of the book series: Operator Theory: Advances and Applications (OT, volume 167)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Teodorescu Transform Decomposition of Multivector Fields on Fractal Hypersurfaces

    • Ricardo Abreu-Blaya, Juan Bory-Reyes, Tania Moreno-García
    Pages 1-16

  3. Metric Dependent Clifford Analysis with Applications to Wavelet Analysis

    • Fred Brackx, Nele De Schepper, Frank Sommen
    Pages 17-67

  4. A Hierarchical Semi-separable Moore-Penrose Equation Solver

    • Patrick Dewilde, Shivkumar Chandrasekaran
    Pages 69-85

  5. Methods from Multiscale Theory and Wavelets Applied to Nonlinear Dynamics

    • Dorin Ervin Dutkay, Palle E. T. Jorgensen
    Pages 87-126

  6. Noncommutative Trigonometry

    • Karl Gustafson
    Pages 127-155

  7. Stationary Random Fields over Graphs and Related Structures

    • Herbert Heyer
    Pages 157-171

  8. Matrix Representations and Numerical Computations of Wavelet Multipliers

    • M. W. Wong, Hongmei Zhu
    Pages 173-182

  9. Clifford Algebra-valued Admissible Wavelets Associated to More than 2-dimensional Euclidean Group with Dilations

    • Jiman Zhao, Lizhong Peng
    Pages 183-190
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Keywords

About this book

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

Editors and Affiliations

  • Department of Mathematics, Ben-Gurion University of the Negev, Beer Sheva, Israel

    Daniel Alpay

  • Institut für Analysis und Scientiific Computing, Technische Universität Wien, Wien, Austria

    Annemarie Luger, Harald Woracek

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