Application Of Holomorphic Functions In Two And Higher Dimensions
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Application of Holomorphic Functions in Two and Higher Dimensions
Author | : Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig |
Publsiher | : Springer |
Total Pages | : 390 |
Release | : 2016-06-20 |
Genre | : Mathematics |
ISBN | : 9783034809641 |
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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 Throughout the book the authors endeavor to present historical references and important personalities.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.
Holomorphic Functions in the Plane and n dimensional Space
Author | : Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig |
Publsiher | : Birkhäuser |
Total Pages | : 394 |
Release | : 2009-09-03 |
Genre | : Mathematics |
ISBN | : 3764391936 |
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Complex analysis nowadays has higher-dimensional analoga: the algebra of complex numbers is replaced then by the non-commutative algebra of real quaternions or by Clifford algebras. During the last 30 years the so-called quaternionic and Clifford or hypercomplex analysis successfully developed to a powerful theory with many applications in analysis, engineering and mathematical physics. This textbook introduces both to classical and higher-dimensional results based on a uniform notion of holomorphy. Historical remarks, lots of examples, figures and exercises accompany each chapter.
Applied Analysis Optimization and Soft Computing
Author | : Tanmoy Som,Debdas Ghosh,Oscar Castillo,Adrian Petrusel,Dayaram Sahu |
Publsiher | : Springer Nature |
Total Pages | : 425 |
Release | : 2023-06-10 |
Genre | : Mathematics |
ISBN | : 9789819905973 |
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This book contains select contributions presented at the International Conference on Nonlinear Applied Analysis and Optimization (ICNAAO-2021), held at the Department of Mathematics Sciences, Indian Institute of Technology (BHU) Varanasi, India, from 21–23 December 2021. The book discusses topics in the areas of nonlinear analysis, fixed point theory, dynamical systems, optimization, fractals, applications to differential/integral equations, signal and image processing, and soft computing, and exposes the young talents with the newer dimensions in these areas with their practical approaches and to tackle the real-life problems in engineering, medical and social sciences. Scientists from the U.S.A., Austria, France, Mexico, Romania, and India have contributed their research. All the submissions are peer reviewed by experts in their fields.
Holomorphic Functions in the Plane and n dimensional Space
Author | : Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig |
Publsiher | : Springer Science & Business Media |
Total Pages | : 407 |
Release | : 2007-11-16 |
Genre | : Mathematics |
ISBN | : 9783764382711 |
Download Holomorphic Functions in the Plane and n dimensional Space Book in PDF, Epub and Kindle
Complex analysis nowadays has higher-dimensional analoga: the algebra of complex numbers is replaced then by the non-commutative algebra of real quaternions or by Clifford algebras. During the last 30 years the so-called quaternionic and Clifford or hypercomplex analysis successfully developed to a powerful theory with many applications in analysis, engineering and mathematical physics. This textbook introduces both to classical and higher-dimensional results based on a uniform notion of holomorphy. Historical remarks, lots of examples, figures and exercises accompany each chapter.
Dirichlet Series and Holomorphic Functions in High Dimensions
Author | : Andreas Defant,Domingo García,Manuel Maestre,Pablo Sevilla-Peris |
Publsiher | : Cambridge University Press |
Total Pages | : 709 |
Release | : 2019-08-08 |
Genre | : Mathematics |
ISBN | : 9781108476713 |
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Using contemporary concepts, this book describes the interaction between Dirichlet series and holomorphic functions in high dimensions.
Quadrature Domains and Their Applications
Author | : Harold S. Shapiro |
Publsiher | : Springer Science & Business Media |
Total Pages | : 312 |
Release | : 2005-01-27 |
Genre | : Mathematics |
ISBN | : 3764371455 |
Download Quadrature Domains and Their Applications Book in PDF, Epub and Kindle
Quadrature domains were singled out about 30 years ago by D. Aharonov and H.S. Shapiro in connection with an extremal problem in function theory. Since then, a series of coincidental discoveries put this class of planar domains at the center of crossroads of several quite independent mathematical theories, e.g., potential theory, Riemann surfaces, inverse problems, holomorphic partial differential equations, fluid mechanics, operator theory. The volume is devoted to recent advances in the theory of quadrature domains, illustrating well the multi-facet aspects of their nature. The book contains a large collection of open problems pertaining to the general theme of quadrature domains.
Complex Analysis Methods Trends and Applications
Author | : Eberhard Lanckau,Wolfgang Tutschke |
Publsiher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 400 |
Release | : 1983-12-31 |
Genre | : Mathematics |
ISBN | : 9783112707753 |
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No detailed description available for "Complex Analysis – Methods, Trends, and Applications".
Geometric Function Theory in One and Higher Dimensions
Author | : Ian Graham |
Publsiher | : CRC Press |
Total Pages | : 572 |
Release | : 2003-03-18 |
Genre | : Mathematics |
ISBN | : 0203911628 |
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This reference details valuable results that lead to improvements in existence theorems for the Loewner differential equation in higher dimensions, discusses the compactness of the analog of the Caratheodory class in several variables, and studies various classes of univalent mappings according to their geometrical definitions. It introduces the in