Описание: 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 Schr?dinger 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 Throughout the book the authors endeavor to present historical references and important personalities.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.
Описание: This book has as its subject the boundary value theory of holomorphic functions in several complex variables, a topic that is just now coming to the forefront of mathematical analysis. For one variable, the topic is classical and rather well understood. In several variables, the necessary understanding of holomorphic functions via partial different
Автор: D. Drasin; C.J. Earle; F.W. Gehring; I. Kra; A. Ma Название: Holomorphic Functions and Moduli I ISBN: 1461396042 ISBN-13(EAN): 9781461396048 Издательство: Springer Рейтинг: Цена: 16769.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The Spring 1986 Program in Geometric Function Theory (GFT) at the Mathematical Sciences Research Institute (MSRI) brought together mathe- maticians interested in Teichmiiller theory, quasiconformal mappings, Kleinian groups, univalent functions and value distribution.
Автор: Andr? Unterberger Название: Quantization and Non-holomorphic Modular Forms ISBN: 3540678611 ISBN-13(EAN): 9783540678618 Издательство: Springer Рейтинг: Цена: 5583.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This is a new approach to the theory of non-holomorphic modular forms, based on ideas from quantization theory or pseudodifferential analysis.
Описание: The subject of this book is Complex Analysis in Several Variables. This text begins at an elementary level with standard local results, followed by a thorough discussion of the various fundamental concepts of "complex convexity" related to the remarkable extension properties of holomorphic functions in more than one variable. It then continues with a comprehensive introduction to integral representations, and concludes with complete proofs of substantial global results on domains of holomorphy and on strictly pseudoconvex domains inC", including, for example, C. Fefferman's famous Mapping Theorem. The most important new feature of this book is the systematic inclusion of many of the developments of the last 20 years which centered around integral representations and estimates for the Cauchy-Riemann equations. In particu- lar, integral representations are the principal tool used to develop the global theory, in contrast to many earlier books on the subject which involved methods from commutative algebra and sheaf theory, and/or partial differ- ential equations. I believe that this approach offers several advantages: (1) it uses the several variable version of tools familiar to the analyst in one complex variable, and therefore helps to bridge the often perceived gap between com- plex analysis in one and in several variables; (2) it leads quite directly to deep global results without introducing a lot of new machinery; and (3) concrete integral representations lend themselves to estimations, therefore opening the door to applications not accessible by the earlier methods.
Автор: David Drasin; C.J. Earle; F.W. Gehring; I. Kra; A. Название: Holomorphic Functions and Moduli II ISBN: 1461396131 ISBN-13(EAN): 9781461396130 Издательство: Springer Рейтинг: Цена: 16769.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The Spring 1986 Program in Geometric Function Theory (GFT) at the Mathematical Sciences Research Institute (MSRI) brought together mathe- maticians interested in Teichmiiller theory, quasiconformal mappings, Kleinian groups, univalent functions and value distribution.
Автор: Frauenfelder Название: The Restricted Three-Body Problem and Holomorphic Curves ISBN: 3319722778 ISBN-13(EAN): 9783319722771 Издательство: Springer Рейтинг: Цена: 16769.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
The book serves as an introduction to holomorphic curves in symplectic manifolds, focusing on the case of four-dimensional symplectizations and symplectic cobordisms, and their applications to celestial mechanics.
The authors study the restricted three-body problem using recent techniques coming from the theory of pseudo-holomorphic curves. The book starts with an introduction to relevant topics in symplectic topology and Hamiltonian dynamics before introducing some well-known systems from celestial mechanics, such as the Kepler problem and the restricted three-body problem. After an overview of different regularizations of these systems, the book continues with a discussion of periodic orbits and global surfaces of section for these and more general systems. The second half of the book is primarily dedicated to developing the theory of holomorphic curves - specifically the theory of fast finite energy planes - to elucidate the proofs of the existence results for global surfaces of section stated earlier. The book closes with a chapter summarizing the results of some numerical experiments related to finding periodic orbits and global surfaces of sections in the restricted three-body problem.
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