By Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig
This ebook offers functions of hypercomplex research to boundary worth and initial-boundary worth difficulties from quite a few components of mathematical physics. provided that quaternion and Clifford research supply traditional and clever how you can input into larger dimensions, it begins 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 useful functionality areas are brought, and an operator calculus in line with ameliorations of the Dirac, Cauchy-Fueter, and Teodorescu operators and diversified 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 process, the Schrödinger equation, and the Beltrami equation. The higher-order equations begin with Riccati-type equations. additional issues contain spatial fluid stream difficulties, picture and multi-channel processing, picture 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 e-book the authors exercise to provide old references and significant personalities. The e-book is meant for a large viewers within the mathematical and engineering sciences and is obtainable to readers with a simple clutch of actual, advanced, and sensible analysis.
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Application of Holomorphic Functions in Two and Higher Dimensions by Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig