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Birkhäuser

Hypercomplex Analysis: New Perspectives and Applications

  • Conference proceedings
  • © 2014

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. Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

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  4. Frank Sommen

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

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  • Covers developments in all directions of hypercomplex analysis
  • Presents new perspectives and current trends for researchers interested in or related to the topic
  • Includes contributions written by leading experts in the field
  • Includes applications (image analysis, mathematical physics and mechanics, etc.) for persons working in these areas
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (15 papers)

  1. Front Matter

    Pages i-vii
    Download chapter PDF

  2. Symmetries and Associated Pairs in Quaternionic Analysis

    • Ricardo Abreu Blaya, Juan Bory Reyes, Alí Guzmán Adán, Uwe Kähler
    Pages 1-18

  3. Generalized Quaternionic Schur Functions in the Ball and Half-space and Krein–Langer Factorization

    • Daniel Alpay, Fabrizio Colombo, Irene Sabadini
    Pages 19-41

  4. The Fock Space in the Slice Hyperholomorphic Setting

    • Daniel Alpay, Fabrizio Colombo, Irene Sabadini, Guy Salomon
    Pages 43-59

  5. Multi M q -monogenic Function in Different Dimension

    • Eusebio Ariza, Antonio Di Teodoro
    Pages 61-73

  6. The Fractional Monogenic Signal

    • Swanhild Bernstein
    Pages 75-88

  7. Weighted Bergman Spaces

    • Carmona L. Luís Javier, Lino Feliciano Reséndis Ocampo, Luis Manuel Tovar Sánchez
    Pages 89-110

  8. On Appell Sets and Verma Modules for \( \mathfrak{sl} \)(2)

    • David Eelbode, Nikolaas Verhulst
    Pages 111-118

  9. Integral Formulas for k-hypermonogenic Functions in ℝ3

    • Sirkka-Liisa Eriksson, Heikki Orelma, Nelson Vieira
    Pages 119-132

  10. Spectral Properties of Compact Normal Quaternionic Operators

    • Riccardo Ghiloni, Valter Moretti, Alessandro Perotti
    Pages 133-143

  11. Three-dimensional Quaternionic Analogue of the Kolosov–Muskhelishvili Formulae

    • Yuri Grigor’ev
    Pages 145-166

  12. On the Continuous Coupling of Finite Elements with Holomorphic Basis Functions

    • Klaus Gürlebeck, Dmitrii Legatiuk
    Pages 167-180

  13. On ψ-hyperholomorphic Functions and a Decomposition of Harmonics

    • Klaus Gürlebeck, Hung Manh Nguyen
    Pages 181-189

  14. Fractional Clifford Analysis

    • Uwe Kähler, Nelson Vieira
    Pages 191-201

  15. Spectral Properties of Differential Equations in Clifford Algebras

    • Yakov Krasnov
    Pages 203-211

  16. Differential Equations in Multicomplex Spaces

    • Daniele C. Struppa, Adrian Vajiac, Mihaela B. Vajiac
    Pages 213-227
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Keywords

About this book

Hypercomplex analysis is the extension of complex analysis to higher dimensions where the concept of a holomorphic function is substituted by the concept of a monogenic function. In recent decades this theory has come to the forefront of higher dimensional analysis. There are several approaches to this: quaternionic analysis which merely uses quaternions, Clifford analysis which relies on Clifford algebras, and generalizations of complex variables to higher dimensions such as split-complex variables. This book includes a selection of papers presented at the session on quaternionic and hypercomplex analysis at the ISAAC conference 2013 in Krakow, Poland. The topics covered represent new perspectives and current trends in hypercomplex analysis and applications to mathematical physics, image analysis and processing, and mechanics.

Editors and Affiliations

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

    Swanhild Bernstein

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

    Uwe Kähler

  • Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

    Irene Sabadini

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

    Frank Sommen

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