By Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig
This ebook provides functions of hypercomplex research to boundary price and initial-boundary price difficulties from quite a few components of mathematical physics. provided that quaternion and Clifford research supply ordinary and clever how you can input into greater dimensions, it begins with quaternion and Clifford types of complicated functionality concept together with sequence expansions with Appell polynomials, in addition to Taylor and Laurent sequence. numerous priceless functionality areas are brought, and an operator calculus in accordance with changes of the Dirac, Cauchy-Fueter, and Teodorescu operators and diversified 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 reminiscent of the Maxwell equations, the Carleman-Bers-Vekua method, the Schrödinger equation, and the Beltrami equation. The higher-order equations begin with Riccati-type equations. additional themes comprise spatial fluid circulation difficulties, photo and multi-channel processing, photo 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 critical personalities. The publication is meant for a large viewers within the mathematical and engineering sciences and is obtainable to readers with a easy snatch of genuine, advanced, and useful analysis.
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Application of Holomorphic Functions in Two and Higher Dimensions by Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig