By Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig
This publication offers functions of hypercomplex research to boundary price and initial-boundary worth difficulties from a variety of parts of mathematical physics. on condition that quaternion and Clifford research supply average and clever how one can input into better dimensions, it starts off 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 important functionality areas are brought, and an operator calculus in keeping with changes of the Dirac, Cauchy-Fueter, and Teodorescu operators and varied decompositions of quaternion Hilbert areas are proved. eventually, hypercomplex Fourier transforms are studied in detail.
All this can be then utilized to first-order partial differential equations equivalent to 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 issues contain spatial fluid stream difficulties, snapshot and multi-channel processing, picture diffusion, linear scale invariant filtering, and others. one of many highlights is the derivation of the third-dimensional Kolosov-Mushkelishvili formulation in linear elasticity.
Throughout the ebook the authors undertaking to give ancient references and demanding 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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