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Hypercomplex Analysis and Applications

  • Conference proceedings
  • © 2011

Overview

Editors:
  1. Irene Sabadini

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

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    You can also search for this editor in PubMed   Google Scholar

  2. Frank Sommen

    1. Fac. Engineering, Dept. Mathematical Analysis, University of Gent, Gent, Belgium

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    You can also search for this editor in PubMed   Google Scholar

  • Among the authors of the contributions there are several first-rate mathematicians
  • The contributed papers will represent the most recent achievements in the area as well as the state-of-the art expositions
  • The contents cover several different aspects of the Hypercomplex analysis
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (19 papers)

  1. Front Matter

    Pages i-vii
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  2. On the Geometry of the Quaternionic Unit Disc

    • Cinzia Bisi, Graziano Gentili
    Pages 1-11

  3. Bounded Perturbations of the Resolvent Operators Associated to the \( \mathcal {F}\)-Spectrum

    • Fabrizio Colombo, Irene Sabadini
    Pages 13-28

  4. Harmonic and Monogenic Functions in Superspace

    • K. Coulembier, H. De Bie, F. Sommen
    Pages 29-41

  5. A Hyperbolic Interpretation of Cauchy-Type Kernels in Hyperbolic Function Theory

    • Sirkka-Liisa Eriksson, Heikki Orelma
    Pages 43-59

  6. Gyrogroups in Projective Hyperbolic Clifford Analysis

    • Milton Ferreira
    Pages 61-80

  7. Invariant Operators of First Order Generalizing the Dirac Operator in 2 Variables

    • Peter Franek
    Pages 81-93

  8. The Zero Sets of Slice Regular Functions and the Open Mapping Theorem

    • Graziano Gentili, Caterina Stoppato
    Pages 95-107

  9. A New Approach to Slice Regularity on Real Algebras

    • Riccardo Ghiloni, Alessandro Perotti
    Pages 109-123

  10. On the Incompressible Viscous Stationary MHD Equations and Explicit Solution Formulas for Some Three-dimensional Radially Symmetric Domai

    • Rolf Sören Kraußhar
    Pages 125-137

  11. The Fischer Decomposition for the H-action and Its Applications

    • Roman Lávička
    Pages 139-148

  12. Bochner’s Formulae for Dunkl-Harmonics and Dunkl-Monogenics

    • Shanshan Li, Minggang Fei
    Pages 149-159

  13. An Invitation to Split Quaternionic Analysis

    • Matvei Libine
    Pages 161-180

  14. On the Hyperderivatives of Moisil–Théodoresco Hyperholomorphic Functions

    • M. Elena Luna-Elizarrarás, Marco A. Macías-Cedeño, Michael Shapiro
    Pages 181-193

  15. Deconstructing Dirac Operators. II: Integral Representation Formulas

    • Mircea Martin
    Pages 195-211

  16. A Differential Form Approach to Dirac Operators on Surfaces

    • Heikki Orelma, Frank Sommen
    Pages 213-232

  17. Killing Tensor Spinor Forms and Their Application in Riemannian Geometry

    • Petr Somberg
    Pages 233-247

  18. Construction of Conformally Invariant Differential Operators

    • VÍt Tuček
    Pages 249-260

  19. Remarks on Holomorphicity in Three Settings: Complex, Quaternionic, and Bicomplex

    • Daniele C. Struppa, Adrian Vajiac, Mihaela B. Vajiac
    Pages 261-274

  20. The Gauss-Lucas Theorem for Regular Quaternionic Polynomials

    • Fabio Vlacci
    Pages 275-282
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Keywords

About this book

The purpose of the volume is to bring forward recent trends of research in hypercomplex analysis. The list of contributors includes first rate mathematicians and young researchers working on several different aspects in quaternionic and Clifford analysis. Besides original research papers, there are papers providing the state-of-the-art of a specific topic, sometimes containing interdisciplinary fields. The intended audience includes researchers, PhD students, postgraduate students who are interested in the field and in possible connection between hypercomplex analysis and other disciplines, including mathematical analysis, mathematical physics, algebra.

Editors and Affiliations

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

    Irene Sabadini

  • Fac. Engineering, Dept. Mathematical Analysis, University of Gent, Gent, Belgium

    Frank Sommen

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