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Application of holomorphic functions...

Gurlebeck, Klaus.

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Application of holomorphic functions in two and higher dimensions

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Application of holomorphic functions in two and higher dimensions/ by Klaus Gurlebeck, Klaus Habetha, Wolfgang Sprossig.
作者:	Gurlebeck, Klaus.
其他作者:	Habetha, Klaus.
出版者:	Basel :Springer Basel : : 2016.,
面頁冊數:	xv, 390 p. :ill. (some col.), digital ;24 cm.
內容註:	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.
Contained By:	Springer eBooks
標題:	Holomorphic functions. -
電子資源:	http://dx.doi.org/10.1007/978-3-0348-0964-1
ISBN:	9783034809641

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

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

700319
Holomorphic functions.

LC Class. No.: QA331

Dewey Class. No.: 515.98

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245 1 0 $a Application of holomorphic functions in two and higher dimensions $h [electronic resource] / $c by Klaus Gurlebeck, Klaus Habetha, Wolfgang Sprossig.
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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 700319
650 1 4 $a Mathematics. $3 515831
650 2 4 $a Integral Transforms, Operational Calculus. $3 897325
650 2 4 $a Functions of a Complex Variable. $3 897310
650 2 4 $a Partial Differential Equations. $3 890899
650 2 4 $a Functional Analysis. $3 893943
700 1 $a Habetha, Klaus. $3 899808
700 1 $a Sprossig, Wolfgang. $3 1050444
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773 0 $t Springer eBooks
856 4 0 $u http://dx.doi.org/10.1007/978-3-0348-0964-1
950 $a Mathematics and Statistics (Springer-11649)