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Synopsis
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-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Throughout the book the authors endeavor to present historical references and important personalities.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.
Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.
À propos de l?auteur
Klaus Gürlebeck, born 1954, Dr. rer. nat. 1984 Technische Hochschule Karl-Marx-Stadt (Chemnitz), Habilitation 1988 TU Karl-Marx-Stadt (Chemnitz), since 1999 Full Prof. Bauhaus-Universität Weimar; co-editor of several international mathematical journals; interested in quaternionic analysis, discrete function theories and applications to partial differential equations.
Klaus Habetha, born 1932, Dr. rer. nat. 1959 Freie Universität Berlin, Habilitation 1962 Technische Universität Berlin, Prof. Technische Universität Berlin, Full Prof. Universität Dortmund and since 1975 RWTH Aachen, here Rector 1987 - 1997, vice-president of German Rectors Conference; co-editor of the journal Complex Variables and elliptic equations until 2007; interested in function theory for partial differential equation.
Wolfgang Sprößig, born 1946, Dr. rer. nat. 1974 Technische Hochschule Karl-Marx-Stadt (Chemnitz) Habilitation 1979 TU Chemnitz, Ass. Prof. TU Chemnitz, since 1986 Full Prof. TU Bergakademie Freiberg, Head of the Institute of Applied Analysis 1993 -2012. Since 1998 Editor-in-Chief of the journal Mathematical Methods in the Applied Sciences, co-editor of several international mathematical journals, interested in hypercomplex analysis and its applications.
Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.
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Application of Holomorphic Functions in Two and Higher Dimensions [Hardcover] Gürlebeck, Klaus; Habetha, Klaus and Sprößig, Wolfgang
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APPLICATION OF HOLOMORPHIC FUNCTIONS IN TWO AND HIGHER DI (2933120726/13.12.2016)
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Application of Holomorphic Functions in Two and Higher Dimensions
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Application of Holomorphic Functions in Two and Higher Dimensions
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Etat : New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Presents a unique hypercomplex strategy for the solution of boundary value problems and initial-boundary value problems in higher dimensionsDetails hypercomplex versions of the Fourier transform and applicationsOffers new approaches to boun. N° de réf. du vendeur 102325254
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Application of Holomorphic Functions in Two and Higher Dimensions
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Buch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - 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.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. N° de réf. du vendeur 9783034809627
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Application of Holomorphic Functions in Two and Higher Dimensions
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Buch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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.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. 408 pp. Englisch. N° de réf. du vendeur 9783034809627
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Application of Holomorphic Functions in Two and Higher Dimensions
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Application of Holomorphic Functions in Two and Higher Dimensions
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Springer Basel, Springer Basel Jun 2016, 2016
ISBN 10 : 303480962X
ISBN 13 : 9783034809627
Neuf
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Vendeur : buchversandmimpf2000, Emtmannsberg, BAYE, Allemagne
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Buch. Etat : Neu. Neuware -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-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.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 408 pp. Englisch. N° de réf. du vendeur 9783034809627
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