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Titlebook: Application of Holomorphic Functions in Two and Higher Dimensions; Klaus Gürlebeck,Klaus Habetha,Wolfgang Spr??ig Book 2016 Springer Inter

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期刊全稱Application of Holomorphic Functions in Two and Higher Dimensions
影響因子2023Klaus Gürlebeck,Klaus Habetha,Wolfgang Spr??ig
視頻videohttp://file.papertrans.cn/160/159121/159121.mp4
發(fā)行地址Presents a unique hypercomplex strategy for the solution of boundary value problems and initial-boundary value problems in higher dimensions.Details hypercomplex versions of the Fourier transform and
圖書封面Titlebook: Application of Holomorphic Functions in Two and Higher Dimensions;  Klaus Gürlebeck,Klaus Habetha,Wolfgang Spr??ig Book 2016 Springer Inter
影響因子.This book presents applications of hypercomplex analysis to boundary value and initial-boundary value problems from various areas of mathematical physics. Given that quaternion and Clifford analysis offer natural and intelligent ways to enter into higher dimensions, it starts with quaternion and Clifford versions of complex function theory including series expansions with Appell polynomials, as well as Taylor and Laurent series. Several necessary function spaces are introduced, and an operator calculus based on modifications of the Dirac, Cauchy-Fueter, and Teodorescu operators and different decompositions of quaternion Hilbert spaces are proved. Finally, hypercomplex Fourier transforms are studied in detail.. .All this is then applied to first-order partial differential equations such as the Maxwell equations, the Carleman-Bers-Vekua system, the Schr?dinger equation, and the Beltrami equation. The higher-order equations start with Riccati-type equations. Further topicsinclude spatial fluid flow problems, image and multi-channel processing, image diffusion, linear scale invariant filtering, and others. One of the highlights is the derivation of the three-dimensional Kolosov-Mushke
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Decompositions,t role in the description of physical relevant equations in the plane and space. In particular, vector fields describe the intensity and direction of a force, the velocity and direction of particles in a moving fluid, or the magnitude and direction of electric and magnetic forces.
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Some initial-boundary value problems,alytic numerical techniques. We start with a brief discussion of strategies for the treatment of time-dependent parabolic problems. Three methods should be considered here: the horizontal method of lines, better known as the Rothe method, the Witt basis approach, and the harmonic extension method. T
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Book 2016sics. Given that quaternion and Clifford analysis offer natural and intelligent ways to enter into higher dimensions, it starts with quaternion and Clifford versions of complex function theory including series expansions with Appell polynomials, as well as Taylor and Laurent series. Several necessar
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