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Application of Holomorphic Functions in Two and Higher Dimensions

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 topics include 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-Mushkelishvili formulas in linear elasticity.

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Detail Information
Series Title
-
Call Number
515.4 GUR a
Publisher
Basel : Birkhäuser Basel.,
Collation
XV, 390
Language
English
ISBN/ISSN
978-3-0348-0964-1
Classification
515.4
Content Type
text
Media Type
computer
Carrier Type
online resource
Edition
Ed. 1
Subject(s)
Integral Transforms
Operational Calculus
Specific Detail Info
-
Statement of Responsibility
Other Information
Cataloger
umi
Source
https://link.springer.com/content/pdf/10.1007/978-3-0348-0964-1.pdf?pdf=button
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