Book: Hypercomplex Analysis and Applications


Hypercomplex Analysis and Applications
Series: Trends in Mathematics
Sabadini, Irene; Sommen, Frank (Eds.)
1st Edition., 2011, VIII, 282 p.
A product of Springer Basel
Hardcover, ISBN 978-3-0346-0245-7
Price: 89,95 €

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

Content Level » Research

Related subjects » AnalysisComputational Science & EngineeringDynamical Systems & Differential EquationsTheoretical, Mathematical & Computational Physics

Contents

C. Bisi and G. Gentili
On the Geometry of the Quaternionic Unit Disc . . . . . . . . . . . . . . . . . . . . . . . . . 1
F. Colombo and I. Sabadini
Bounded Perturbations of the Resolvent Operators Associated to the
F-Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
K. Coulembier, H. De Bie and F. Sommen
Harmonic and Monogenic Functions in Superspace . . . . . . . . . . . . . . . . . . . . . .29
S.-L. Eriksson and H. Orelma
A Hyperbolic Interpretation of Cauchy-Type Kernels in Hyperbolic
Function Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
M. Ferreira
Gyrogroups in Projective Hyperbolic Clifford Analysis . . . . . . . . . . . . . . . . . . 61
P. Franek
Invariant Operators of First Order Generalizing the Dirac Operator
in 2 Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
G. Gentili and C. Stoppato
The Zero Sets of Slice Regular Functions and the Open Mapping
Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
R. Ghiloni and A. Perotti
A New Approach to Slice Regularity on Real Algebras . . . . . . . . . . . . . . . . .109
R.S. Kraußhar
On the Incompressible Viscous Stationary MHD Equations and Explicit
Solution Formulas for Some Three-dimensional Radially Symmetric
Domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
R. L´aviˇcka
The Fischer Decomposition for the H-action and Its Applications . . . . . .139
S. Li and M. Fei
Bochner’s Formulae for Dunkl-Harmonics and Dunkl-Monogenics . . . . . . 149
M. Libine
An Invitation to Split Quaternionic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . .161
M.E. Luna-Elizarrar´as, M.A. Mac´ıas-Cede˜no and M. Shapiro
On the Hyperderivatives of Moisil–Th´eodoresco Hyperholomorphic
Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
M. Martin
Deconstructing Dirac Operators. II: Integral Representation Formulas . 195
H. Orelma and F. Sommen
A Differential Form Approach to Dirac Operators on Surfaces . . . . . . . . . 213
P. Somberg
Killing Tensor Spinor Forms and Their Application in Riemannian
Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
V. Tuˇcek
Construction of Conformally Invariant Differential Operators . . . . . . . . . . 249
D.C. Struppa, A. Vajiac and M.B. Vajiac
Remarks on Holomorphicity in Three Settings: Complex,
Quaternionic, and Bicomplex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
F. Vlacci
The Gauss-Lucas Theorem for Regular Quaternionic Polynomials . . . . . . 275

Source: http://www.springer.com/mathematics/dynamical+systems/book/978-3-0346-0245-7

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