Application of Holomorphic Functions in Two and Higher Dimensions
Klaus Gürlebeck
Sold by AHA-BUCH GmbH, Einbeck, Germany
AbeBooks Seller since 14 August 2006
New - Hardcover
Condition: New
Quantity: 1 available
Add to basketSold by AHA-BUCH GmbH, Einbeck, Germany
AbeBooks Seller since 14 August 2006
Condition: New
Quantity: 1 available
Add to basketDruck 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Kolosov-Mushkelishvili formulas in linear elasticity.Throughout the book the authors endeavor to present historical references and important personalities.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.
Seller Inventory # 9783034809627
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.
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.
"About this title" may belong to another edition of this title.
General Terms and Conditions and Customer Information / Privacy Policy
I. General Terms and Conditions
§ 1 Basic provisions
(1) The following terms and conditions apply to all contracts that you conclude with us as a provider (AHA-BUCH GmbH) via the Internet platforms AbeBooks and/or ZVAB. Unless otherwise agreed, the inclusion of any of your own terms and conditions used by you will be objected to
(2) A consumer within the meaning of the following regulations is any natural person who concludes...
We ship your order after we received them
for articles on hand latest 24 hours,
for articles with overnight supply latest 48 hours.
In case we need to order an article from our supplier our dispatch time depends on the reception date of the articles, but the articles will be shipped on the same day.
Our goal is to send the ordered articles in the fastest, but also most efficient and secure way to our customers.
Order quantity | 2 to 4 business days | 2 to 4 business days |
---|---|---|
First item | £ 12.16 | £ 12.16 |
Delivery times are set by sellers and vary by carrier and location. Orders passing through Customs may face delays and buyers are responsible for any associated duties or fees. Sellers may contact you regarding additional charges to cover any increased costs to ship your items.