Topics in Clifford Analysis - Special Volume in Honor of Wolfgang Sprößig

Description

Quaternionic and Clifford analysis are an extension of complex analysis into higher dimensions. The unique starting point of Wolfgang Sprößig’s work was the application of quaternionic analysis to elliptic differential equations and boundary value problems. Over the years, Clifford analysis has become a broad-based theory with a variety of applications both inside and outside of mathematics, such as higher-dimensional function theory, algebraic structures, generalized polynomials, applications of elliptic boundary value problems, wavelets, image processing, numerical and discrete analysis. The aim of this volume is to provide an essential overview of modern topics in Clifford analysis, presented by specialists in the field, and to honor the valued contributions to Clifford analysis made by Wolfgang Sprößig throughout his career. Front Matter ....Pages i-xxi Front Matter ....Pages 1-1 Cauchy’s Formula in Clifford Analysis: An Overview (Fred Brackx, Hennie De Schepper, Roman Lávička, Vladimir Souček)....Pages 3-23 Quaternionic Hyperbolic Function Theory (Sirkka-Liisa Eriksson, Heikki Orelma)....Pages 25-52 Slice Regularity and Harmonicity on Clifford Algebras (Alessandro Perotti)....Pages 53-73 Some Notions of Subharmonicity over the Quaternions (Caterina Stoppato)....Pages 75-101 Front Matter ....Pages 103-103 A Fatou Theorem and Poisson’s Integral Representation Formula for Elliptic Systems in the Upper Half-Space (Juan José Marín, José María Martell, Dorina Mitrea, Irina Mitrea, Marius Mitrea)....Pages 105-124 Hardy Spaces for the Three-Dimensional Vekua Equation (Briceyda B. Delgado, R. Michael Porter)....Pages 125-140 Radial and Angular Derivatives of Distributions (Fred Brackx)....Pages 141-171 Applications of Parabolic Dirac Operators to the Instationary Viscous MHD Equations on Conformally Flat Manifolds (Paula Cerejeiras, Uwe Kähler, R. Sören Kraußhar)....Pages 173-190 Generalized Riesz Transforms, Quasi-Monogenic Functions and Frames (Swanhild Bernstein, Sandra Schufmann)....Pages 191-218 Front Matter ....Pages 219-219 Quaternionic Operator Calculus for Boundary Value Problems of Micropolar Elasticity (Klaus Gürlebeck, Dmitrii Legatiuk)....Pages 221-234 Constructive Orthonormalisation of Monogenic Polynomials on a Finite Cylinder (Sebastian Bock, Dmitrii Legatiuk)....Pages 235-250 Comments on an Orthogonal Family of Monogenic Functions on Spheroidal Domains (Joaõ Morais)....Pages 251-266 Newton’s Approach to General Algebraic Equations over Clifford Algebras (Drahoslava Janovská, Gerhard Opfer)....Pages 267-276 Front Matter ....Pages 277-277 Connections in Euclidean and Non-commutative Geometry (Viktor Abramov, Olga Liivapuu)....Pages 279-311 Conformal Parametrisation of Loxodromes by Triples of Circles (Vladimir V. Kisil, James Reid)....Pages 313-330 Automorphic Forms and Dirac Operators on Conformally Flat Manifolds (Rolf Sören Kraußhar)....Pages 331-345 Higher Order Fermionic and Bosonic Operators (Chao Ding, Raymond Walter, John Ryan)....Pages 347-380 Clifford Möbius Geometry (Craig A. Nolder)....Pages 381-394 Separation of Variables in the Semistable Range (Roman Lávička)....Pages 395-403 Variety of Idempotents in Nonassociative Algebras (Yakov Krasnov, Vladimir G. Tkachev)....Pages 405-436 Front Matter ....Pages 437-437 Relativistic Wave Equations on the Lattice: An Operational Perspective (Nelson Faustino)....Pages 439-469 Cauchy-Pompeiu Formula for Discrete Monogenic Functions (Guangbin Ren, Zeping Zhu)....Pages 471-486 A Useful Transformation for Solving the Discrete Beltrami Equation and Reducing a Difference Equation of Second Order to a System of Equations of First Order (Angela Hommel)....Pages 487-503