By Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig
This booklet provides purposes of hypercomplex research to boundary price and initial-boundary worth difficulties from numerous parts of mathematical physics. provided that quaternion and Clifford research provide typical and clever how you can input into better dimensions, it begins with quaternion and Clifford models of complicated functionality thought together with sequence expansions with Appell polynomials, in addition to Taylor and Laurent sequence. a number of invaluable functionality areas are brought, and an operator calculus in response to transformations of the Dirac, Cauchy-Fueter, and Teodorescu operators and various 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 resembling the Maxwell equations, the Carleman-Bers-Vekua process, the Schrödinger equation, and the Beltrami equation. The higher-order equations commence with Riccati-type equations. additional subject matters contain spatial fluid movement difficulties, photograph and multi-channel processing, picture 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 ebook the authors recreation to offer ancient references and demanding personalities. The ebook is meant for a large viewers within the mathematical and engineering sciences and is on the market to readers with a simple seize of genuine, complicated, and sensible analysis.
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