图书简介

Part I - Clifford analysis theories.-Cauchy’s formula in Clifford analysis: An Overview.-Quaternionic Hyperbolic Function Theory.-Slice Regular and Harmonicity in Clifford Analysis.-Some notions of Subharmonicity over the Quaternions.-Part II - Applications to Elliptic Partial Differential Equations.-A Fatou Theorem and Poisson’s Integral Representation Formula for Elliptic Systems in the Upper-Half Space.-Hardy Spaces for Three-Dimensional Vekua Equation.-Radial and Angular Derivatives of Distributions.- Applications of Parabolic Dirac Operators to the Instationary Viscous MHD Equations on Conformally Flat Manifolds.-Generalized Riesz Transforms, Quasi-Monogenic Functions and Frames.-Part III - Monogenic Polynomials and Numerical Methods.-Quaternionic Operator Calculus for Boundary Value Problems of Micropolar Elasticity.-Constructive Orthonormalization of Monogenic Polynomials on a Finite Cylinder.- Comments on an Orthogonal Family of Monogenic Functions on Spheroidal Domains.-Newton’s Approach to General Algebra Equations over Clifford Algebras.-Part IV - Differential Geometry.-Connections in Euclidean and Non-Commutative Geometry.-Conformal Parametrisation of Loxodroms by Tripels of Circles.-Automorphic Forms and Dirac Operators on Conformally Flat manifolds.-Higher order Fermionic and Bosonic Operators.-Clifford Möbius Geometry.-Separation of Variables in the Semistable Range.-Variety of Idempotents in Nonassociative Algebras.-Part V - Discrete Clifford Analysis.-Relativistic Wave Equations on the Lattice: An Operational Perspective.-Cauchy-Pompeiu Formula for Discrete Monogenic Functions.-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.

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