| 期刊全称 | Application of Holomorphic Functions in Two and Higher Dimensions | | 影响因子2023 | Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig | | 视频video | | | 发行地址 | 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 | | 图书封面 |  | | 影响因子 | .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 Schrödinger 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 | | Pindex | Book 2016 |
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发表于 2025-3-21 18:58:29
