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Wavelets, Multiscale Systems and Hypercomplex Analysis

  • Daniel Alpay
  • Annemarie Luger
  • Harald Woracek

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

Table of contents

  1. Front Matter
    Pages i-xi
  2. Ricardo Abreu-Blaya, Juan Bory-Reyes, Tania Moreno-García
    Pages 1-16
  3. Fred Brackx, Nele De Schepper, Frank Sommen
    Pages 17-67
  4. Patrick Dewilde, Shivkumar Chandrasekaran
    Pages 69-85
  5. Dorin Ervin Dutkay, Palle E. T. Jorgensen
    Pages 87-126
  6. Karl Gustafson
    Pages 127-155

About this book

Introduction

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

Keywords

Clifford analysis Complex analysis Hypercomplex analysis Nonlinear dynamics Operator theory Random field System theory Teodorescu transform Wavelets analysis

Editors and affiliations

  • Daniel Alpay
    • 1
  • Annemarie Luger
    • 2
  • Harald Woracek
    • 2
  1. 1.Department of MathematicsBen-Gurion University of the NegevBeer ShevaIsrael
  2. 2.Institut für Analysis und Scientiific ComputingTechnische Universität WienWienAustria

Bibliographic information