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Application of holomorphic functions...

Gurlebeck, Klaus.

Application of holomorphic functions in two and higher dimensions

Record Type:	Electronic resources : Monograph/item
Title/Author:	Application of holomorphic functions in two and higher dimensionsby Klaus Gurlebeck, Klaus Habetha, Wolfgang Sprossig.
Author:	Gurlebeck, Klaus.
other author:	Habetha, Klaus.
Published:	Basel :Springer Basel :2016.
Description:	xv, 390 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Holomorphic functions.
Online resource:	http://dx.doi.org/10.1007/978-3-0348-0964-1
ISBN:	9783034809641$q(electronic bk.)

Application of holomorphic functions in two and higher dimensions
Gurlebeck, Klaus.

Application of holomorphic functions in two and higher dimensions[electronic resource] /by Klaus Gurlebeck, Klaus Habetha, Wolfgang Sprossig. - Basel :Springer Basel :2016. - xv, 390 p. :ill. (some col.), digital ;24 cm.

1.Basic Properties of Holomorphic Functions -- 2.Conformal and Quasi-conformal Mappings -- 3.Function Theoretic Function spaces -- 4.Operator Calculus -- 5.Decompositions -- 6.Some First Order Systems of Partial Differential Equations -- 7.Boundary Value Problems of Second Order Partial Differential Equations -- 8.Some Initial-boundary Value Problems -- 9.Riemann-Hilbert Problems -- 10.Initial Boundary Value Problems on the Sphere -- 11.Fourier Transforms -- Bibliography -- Index.

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 Schrodinger 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. Throughout the book the authors endeavor to present historical references and important personalities. The book is intended for a wide audience in the mathematical and engineering sciences and is accessible to readers with a basic grasp of real, complex, and functional analysis.

ISBN: 9783034809641$q(electronic bk.)

Standard No.: 10.1007/978-3-0348-0964-1doiSubjects--Topical Terms:

275778
Holomorphic functions.

LC Class. No.: QA331

Dewey Class. No.: 515.98

Application of holomorphic functions in two and higher dimensions
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300 $a xv, 390 p. : $b ill. (some col.), digital ; $c 24 cm.
505 0 $a 1.Basic Properties of Holomorphic Functions -- 2.Conformal and Quasi-conformal Mappings -- 3.Function Theoretic Function spaces -- 4.Operator Calculus -- 5.Decompositions -- 6.Some First Order Systems of Partial Differential Equations -- 7.Boundary Value Problems of Second Order Partial Differential Equations -- 8.Some Initial-boundary Value Problems -- 9.Riemann-Hilbert Problems -- 10.Initial Boundary Value Problems on the Sphere -- 11.Fourier Transforms -- Bibliography -- Index.
520 $a 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 Schrodinger 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. Throughout the book the authors endeavor to present historical references and important personalities. The book is intended for a wide audience in the mathematical and engineering sciences and is accessible to readers with a basic grasp of real, complex, and functional analysis.
650 0 $a Holomorphic functions. $3 275778
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Integral Transforms, Operational Calculus. $3 275781
650 2 4 $a Functions of a Complex Variable. $3 275780
650 2 4 $a Partial Differential Equations. $3 274075
650 2 4 $a Functional Analysis. $3 274845
700 1 $a Habetha, Klaus. $3 275775
700 1 $a Sprossig, Wolfgang. $3 678654
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856 4 0 $u http://dx.doi.org/10.1007/978-3-0348-0964-1
950 $a Mathematics and Statistics (Springer-11649)