By Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig
This publication provides functions of hypercomplex research to boundary worth and initial-boundary worth difficulties from numerous parts of mathematical physics. provided that quaternion and Clifford research supply usual and clever how one can input into better dimensions, it begins with quaternion and Clifford types of advanced functionality idea together with sequence expansions with Appell polynomials, in addition to Taylor and Laurent sequence. a number of valuable functionality areas are brought, and an operator calculus in response to ameliorations of the Dirac, Cauchy-Fueter, and Teodorescu operators and various decompositions of quaternion Hilbert areas are proved. ultimately, hypercomplex Fourier transforms are studied in detail.
All this is often 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. additional themes contain spatial fluid circulation difficulties, snapshot and multi-channel processing, photograph diffusion, linear scale invariant filtering, and others. one of many highlights is the derivation of the three-d Kolosov-Mushkelishvili formulation in linear elasticity.
Throughout the booklet the authors undertaking to give historic references and critical personalities. The e-book is meant for a large viewers within the mathematical and engineering sciences and is on the market to readers with a uncomplicated 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