Hypercomplex Analysis and Applications

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

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.

• partial differential equations

• 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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