By Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig
This e-book offers functions of hypercomplex research to boundary price and initial-boundary worth difficulties from a number of components of mathematical physics. provided that quaternion and Clifford research provide normal and clever how you can input into larger dimensions, it begins with quaternion and Clifford types of complicated functionality idea together with sequence expansions with Appell polynomials, in addition to Taylor and Laurent sequence. a number of valuable functionality areas are brought, and an operator calculus in keeping with alterations 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 can be then utilized to first-order partial differential equations similar to the Maxwell equations, the Carleman-Bers-Vekua process, the Schrödinger equation, and the Beltrami equation. The higher-order equations begin with Riccati-type equations. extra issues comprise spatial fluid movement difficulties, photograph 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 publication the authors recreation to give historic references and critical personalities. The ebook is meant for a large viewers within the mathematical and engineering sciences and is offered to readers with a simple seize of genuine, complicated, and practical analysis.
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Application of Holomorphic Functions in Two and Higher Dimensions by Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig