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Hypercomplex analysis and applications

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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. </p>

The intended audience includes researchers, PhD students and postgraduate students who are interested in the field and in connections between hypercomplex analysis and other disciplines, in particular mathematical analysis, mathematical physics, and algebra.</p>

Contributors: </p>

C. Bisi, F. Colombo, K. Coulembier, H. De Bie, S.-L. Eriksson, M. Fei, M. Ferreira, P. Franek, G. Gentili, R. Ghiloni, R.S. Kraußhar, R. Lávička, S. Li, M. Libine, M.E. Luna-Elizarrarás,

M.A. Macías-Cedeño, M. Martin, H. Orelma, A. Perotti, I. Sabadini, M. Shapiro, P. Somberg, F. Sommen, C. Stoppato, D.C. Struppa, V. Tuček, A. Vajiac, M.B. Vajiac, F. Vlacci

M.A. Macías-Cedeño, M. Martin, H. Orelma, A. Perotti, I. Sabadini, M. Shapiro, P. Somberg, F. Sommen, C. Stoppato, D.C. Struppa, V. Tuček, A. Vajiac, M.B. Vajiac, F. Vlacci

Author(s): Cinzia Bisi, Graziano Gentili (auth.), Irene Sabadini, Frank Sommen (eds.)
Series: Trends in Mathematics
Edition: 1
Publisher: Birkhäuser Basel
Year: 2011

Language: English
Pages: 284
Tags: Partial Differential Equations;Mathematical Methods in Physics;Abstract Harmonic Analysis;Numerical Analysis

Front Matter....Pages i-vii
On the Geometry of the Quaternionic Unit Disc....Pages 1-11
Bounded Perturbations of the Resolvent Operators Associated to the $$ \mathcal {F}$$ -Spectrum....Pages 13-28
Harmonic and Monogenic Functions in Superspace....Pages 29-41
A Hyperbolic Interpretation of Cauchy-Type Kernels in Hyperbolic Function Theory....Pages 43-59
Gyrogroups in Projective Hyperbolic Clifford Analysis....Pages 61-80
Invariant Operators of First Order Generalizing the Dirac Operator in 2 Variables....Pages 81-93
The Zero Sets of Slice Regular Functions and the Open Mapping Theorem....Pages 95-107
A New Approach to Slice Regularity on Real Algebras....Pages 109-123
On the Incompressible Viscous Stationary MHD Equations and Explicit Solution Formulas for Some Three-dimensional Radially Symmetric Domai....Pages 125-137
The Fischer Decomposition for the H -action and Its Applications....Pages 139-148
Bochner’s Formulae for Dunkl-Harmonics and Dunkl-Monogenics....Pages 149-159
An Invitation to Split Quaternionic Analysis....Pages 161-180
On the Hyperderivatives of Moisil–Théodoresco Hyperholomorphic Functions....Pages 181-193
Deconstructing Dirac Operators. II: Integral Representation Formulas....Pages 195-211
A Differential Form Approach to Dirac Operators on Surfaces....Pages 213-232
Killing Tensor Spinor Forms and Their Application in Riemannian Geometry....Pages 233-247
Construction of Conformally Invariant Differential Operators....Pages 249-260
Remarks on Holomorphicity in Three Settings: Complex, Quaternionic, and Bicomplex....Pages 261-274
The Gauss-Lucas Theorem for Regular Quaternionic Polynomials....Pages 275-282