Topics in Clifford Analysis

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.