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Birkhäuser

Modern Trends in Hypercomplex Analysis

  • Conference proceedings
  • © 2016

Overview

Editors:
  1. Swanhild Bernstein

    1. Institute of Applied Analysis, TU Bergakademie Freiberg, Freiberg, Germany

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  2. Uwe Kähler

    1. Departamento de Matemática, Universidade de Aveiro, Aveiro, Portugal

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  3. Irene Sabadini

    1. Dip. di Matematica, Politecnico di Milano, Milano, Italy

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  4. Franciscus Sommen

    1. Department of Mathematical Analysis, Ghent University, Gent, Belgium

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  • Presents recent developments in all directions of hypercomplex analysis
  • Shares new perspectives and current trends for researchers interested in/or related to the topic
  • Features an exposition of applications (image analysis, mathematical physics and mechanics, etc.) for persons working in these areas as well as easily accessible for non-specialists

Part of the book series: Trends in Mathematics (TM)

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Table of contents (15 papers)

  1. Front Matter

    Pages i-vii
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  2. Cauchy–Pompeiu Formula for Multi-meta-weighted-monogenic Functions of first class

    • Eusebio Ariza García, Antonio Di Teodoro
    Pages 1-17

  3. Greedy Algorithms and Rational Approximation in One and Several Variables

    • Laurent Baratchart, Wei-Xiong Mai, Tao Qian
    Pages 19-33

  4. A. Kolmogorov and M. Riesz Theorems for Octonion-valued Monogenic Functions

    • Sultan Catto, Alexander Kheyfits, David Tepper
    Pages 35-46

  5. Compressed Sensing with Nonlinear Fourier Atoms

    • Paula Cerejeiras, Qiuhui Chen, Narciso Gomes, Stefan Hartmann
    Pages 47-77

  6. Script Geometry

    • Paula Cerejeiras, Uwe Kähler, Franciscus Sommen, Adrian Vajiac
    Pages 79-110

  7. A Panorama on Quaternionic Spectral Theory and Related Functional Calculi

    • Fabrizio Colombo, David P. Kimsey
    Pages 111-142

  8. Models for Some Irreducible Representations of \(\mathfrak{so}(m, \mathbb{C})\) in Discrete Clifford Analysis

    • Hilde De Ridder, Tim Raeymaekers
    Pages 143-159

  9. Gegenbauer Type Polynomial Solutions for the Higher Spin Laplace Operator

    • David Eelbode, Tim Janssens
    Pages 161-174

  10. A New Cauchy Type Integral Formula for Quaternionic k-hypermonogenic Functions

    • Sirkka-Liisa Eriksson, Heikki Orelma
    Pages 175-189

  11. Eigenfunctions and Fundamental Solutions of the Caputo Fractional Laplace and Dirac Operators

    • Milton Ferreira, Nelson Vieira
    Pages 191-202

  12. Three-dimensional Analogue of Kolosov–Muskhelishvili Formulae

    • Yuri Grigor’ev
    Pages 203-215

  13. On Some Properties of Pseudo-complex Polynomials

    • Klaus Gürlebeck, Dmitrii Legatiuk
    Pages 217-226

  14. Slice Regular Functions on Regular Quadratic Cones of Real Alternative Algebras

    • Guangbin Ren, Xieping Wang, Zhenghua Xu
    Pages 227-245

  15. Differential Forms and Clifford Analysis

    • Irene Sabadini, Franciscus Sommen
    Pages 247-263

  16. Examples of Morphological Calculus

    • Franciscus Sommen
    Pages 265-310
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About this book

This book contains a selection of papers presented at the session "Quaternionic and Clifford Analysis" at the 10th ISAAC Congress held in Macau in August 2015. The covered topics represent the state-of-the-art as well as new trends in hypercomplex analysis and its applications.

Editors and Affiliations

  • Institute of Applied Analysis, TU Bergakademie Freiberg, Freiberg, Germany

    Swanhild Bernstein

  • Departamento de Matemática, Universidade de Aveiro, Aveiro, Portugal

    Uwe Kähler

  • Dip. di Matematica, Politecnico di Milano, Milano, Italy

    Irene Sabadini

  • Department of Mathematical Analysis, Ghent University, Gent, Belgium

    Franciscus Sommen

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