By Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig
This publication offers purposes of hypercomplex research to boundary price and initial-boundary worth difficulties from a number of parts of mathematical physics. provided that quaternion and Clifford research supply average and clever how one can input into larger dimensions, it starts off with quaternion and Clifford types of advanced functionality concept together with sequence expansions with Appell polynomials, in addition to Taylor and Laurent sequence. a number of beneficial functionality areas are brought, and an operator calculus in response to ameliorations of the Dirac, Cauchy-Fueter, and Teodorescu operators and varied decompositions of quaternion Hilbert areas are proved. ultimately, hypercomplex Fourier transforms are studied in detail.
All this can be then utilized to first-order partial differential equations resembling the Maxwell equations, the Carleman-Bers-Vekua approach, the Schrödinger equation, and the Beltrami equation. The higher-order equations begin with Riccati-type equations. extra themes contain spatial fluid movement difficulties, photograph and multi-channel processing, snapshot diffusion, linear scale invariant filtering, and others. one of many highlights is the derivation of the 3-dimensional Kolosov-Mushkelishvili formulation in linear elasticity.
Throughout the booklet the authors undertaking to give historic references and demanding personalities. The publication is meant for a large viewers within the mathematical and engineering sciences and is available to readers with a easy clutch of genuine, complicated, and sensible analysis.
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Additional resources for Application of Holomorphic Functions in Two and Higher Dimensions
Application of Holomorphic Functions in Two and Higher Dimensions by Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig