By Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig
This ebook provides functions of hypercomplex research to boundary price and initial-boundary worth difficulties from a number of components of mathematical physics. on condition that quaternion and Clifford research supply average and clever how you can input into greater dimensions, it starts off with quaternion and Clifford models of advanced functionality thought together with sequence expansions with Appell polynomials, in addition to Taylor and Laurent sequence. a number of precious functionality areas are brought, and an operator calculus according to ameliorations of the Dirac, Cauchy-Fueter, and Teodorescu operators and diverse decompositions of quaternion Hilbert areas are proved. eventually, 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 commence with Riccati-type equations. additional subject matters 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 third-dimensional Kolosov-Mushkelishvili formulation in linear elasticity.
Throughout the ebook the authors exercise to offer old references and demanding personalities. The e-book is meant for a large viewers within the mathematical and engineering sciences and is available to readers with a simple take hold of of genuine, complicated, and sensible analysis.
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Application of Holomorphic Functions in Two and Higher Dimensions by Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig
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