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Application Of Holomorphic Functions In Two And Higher Dimensions
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Book Synopsis Application of Holomorphic Functions in Two and Higher Dimensions by : Klaus Gürlebeck
Download or read book Application of Holomorphic Functions in Two and Higher Dimensions written by Klaus Gürlebeck and published by Springer. This book was released on 2016-06-20 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Throughout the book the authors endeavor to present historical references and important personalities.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.
Book Synopsis Dirichlet Series and Holomorphic Functions in High Dimensions by : Andreas Defant
Download or read book Dirichlet Series and Holomorphic Functions in High Dimensions written by Andreas Defant and published by Cambridge University Press. This book was released on 2019-08-08 with total page 709 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using contemporary concepts, this book describes the interaction between Dirichlet series and holomorphic functions in high dimensions.
Book Synopsis Applied Analysis, Optimization and Soft Computing by : Tanmoy Som
Download or read book Applied Analysis, Optimization and Soft Computing written by Tanmoy Som and published by Springer Nature. This book was released on 2023-06-10 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Holomorphic Functions in the Plane and n-dimensional Space by : Klaus Gürlebeck
Download or read book Holomorphic Functions in the Plane and n-dimensional Space written by Klaus Gürlebeck and published by Springer Science & Business Media. This book was released on 2007-11-16 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Quadrature Domains and Their Applications by : Harold S. Shapiro
Download or read book Quadrature Domains and Their Applications written by Harold S. Shapiro and published by Springer Science & Business Media. This book was released on 2005-01-27 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Complex Analysis – Methods, Trends, and Applications by : Eberhard Lanckau
Download or read book Complex Analysis – Methods, Trends, and Applications written by Eberhard Lanckau and published by Walter de Gruyter GmbH & Co KG. This book was released on 1983-12-31 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Complex Analysis – Methods, Trends, and Applications".
Book Synopsis Encyclopaedia of Mathematics by : Michiel Hazewinkel
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first Supplementary volume to Kluwer's highly acclaimed Encyclopaedia of Mathematics. This additional volume contains nearly 600 new entries written by experts and covers developments and topics not included in the already published 10-volume set. These entries have been arranged alphabetically throughout. A detailed index is included in the book. This Supplementary volume enhances the existing 10-volume set. Together, these eleven volumes represent the most authoritative, comprehensive up-to-date Encyclopaedia of Mathematics available.
Book Synopsis Holomorphic Functions and Integral Representations in Several Complex Variables by : R. Michael Range
Download or read book Holomorphic Functions and Integral Representations in Several Complex Variables written by R. Michael Range and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Spectral Theory on the S-Spectrum for Quaternionic Operators by : Fabrizio Colombo
Download or read book Spectral Theory on the S-Spectrum for Quaternionic Operators written by Fabrizio Colombo and published by Springer. This book was released on 2019-01-04 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this monograph is the quaternionic spectral theory based on the notion of S-spectrum. With the purpose of giving a systematic and self-contained treatment of this theory that has been developed in the last decade, the book features topics like the S-functional calculus, the F-functional calculus, the quaternionic spectral theorem, spectral integration and spectral operators in the quaternionic setting. These topics are based on the notion of S-spectrum of a quaternionic linear operator. Further developments of this theory lead to applications in fractional diffusion and evolution problems that will be covered in a separate monograph.
Book Synopsis Theory Of Complex Variable by : R.K. Pandey
Download or read book Theory Of Complex Variable written by R.K. Pandey and published by Discovery Publishing House. This book was released on 2007 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents: Algebra of Complex Number, Functions of Complex Number, Limit and Continuity, Analytic Functions, Complex Integration, Cauchy Integral Theorem, Contour Integration, Series in Complex Number, Taylor and Laurent Series.
Book Synopsis An Introduction to Multicomplex SPates and Functions by : Price
Download or read book An Introduction to Multicomplex SPates and Functions written by Price and published by Routledge. This book was released on 2018-05-11 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rather pretty little book, written in the form of a text but more likely to be read simply for pleasure, in which the author (Professor Emeritus of Mathematics at the U. of Kansas) explores the analog of the theory of functions of a complex variable which comes into being when the complexes are re
Book Synopsis An Introduction to Multicomplex Spaces and Functions by : Price
Download or read book An Introduction to Multicomplex Spaces and Functions written by Price and published by CRC Press. This book was released on 1990-10-23 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rather pretty little book, written in the form of a text but more likely to be read simply for pleasure, in which the author (Professor Emeritus of Mathematics at the U. of Kansas) explores the analog of the theory of functions of a complex variable which comes into being when the complexes are re
Book Synopsis Holomorphic Curves in Low Dimensions by : Chris Wendl
Download or read book Holomorphic Curves in Low Dimensions written by Chris Wendl and published by Springer. This book was released on 2018-06-28 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides an accessible introduction to the applications of pseudoholomorphic curves in symplectic and contact geometry, with emphasis on dimensions four and three. The first half of the book focuses on McDuff's characterization of symplectic rational and ruled surfaces, one of the classic early applications of holomorphic curve theory. The proof presented here uses the language of Lefschetz fibrations and pencils, thus it includes some background on these topics, in addition to a survey of the required analytical results on holomorphic curves. Emphasizing applications rather than technical results, the analytical survey mostly refers to other sources for proofs, while aiming to provide precise statements that are widely applicable, plus some informal discussion of the analytical ideas behind them. The second half of the book then extends this program in two complementary directions: (1) a gentle introduction to Gromov-Witten theory and complete proof of the classification of uniruled symplectic 4-manifolds; and (2) a survey of punctured holomorphic curves and their applications to questions from 3-dimensional contact topology, such as classifying the symplectic fillings of planar contact manifolds. This book will be particularly useful to graduate students and researchers who have basic literacy in symplectic geometry and algebraic topology, and would like to learn how to apply standard techniques from holomorphic curve theory without dwelling more than necessary on the analytical details. This book is also part of the Virtual Series on Symplectic Geometry http://www.springer.com/series/16019
Book Synopsis Geometric Function Theory in Higher Dimension by : Filippo Bracci
Download or read book Geometric Function Theory in Higher Dimension written by Filippo Bracci and published by Springer. This book was released on 2018-03-24 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book collects the most relevant outcomes from the INdAM Workshop “Geometric Function Theory in Higher Dimension” held in Cortona on September 5-9, 2016. The Workshop was mainly devoted to discussions of basic open problems in the area, and this volume follows the same line. In particular, it offers a selection of original contributions on Loewner theory in one and higher dimensions, semigroups theory, iteration theory and related topics. Written by experts in geometric function theory in one and several complex variables, it focuses on new research frontiers in this area and on challenging open problems. The book is intended for graduate students and researchers working in complex analysis, several complex variables and geometric function theory.
Book Synopsis A Gateway to Number Theory: Applying the Power of Algebraic Curves by : Keith Kendig
Download or read book A Gateway to Number Theory: Applying the Power of Algebraic Curves written by Keith Kendig and published by American Mathematical Soc.. This book was released on 2021-04-23 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: Challenge: Can you find all the integers a, b, c satisfying 2a2+3b2=5c2? Looks simple, and there are in fact a number of easy solutions. But most of them turn out to be anything but obvious! There are infinitely many possibilities, and as any computer will tell you, each of a, b, c will usually be large. So the challenge remains … Find all integers a a, b, c satisfying 2a2+3b2=5c2 A major advance in number theory means this book can give an easy answer to this and countless similar questions. The idea behind the approach is transforming a degree-two equation in integer variables a, b, c into a plane curve defined by a polynomial. Working with the curve makes obtaining solutions far easier, and the geometric solutions then get translated back into integers. This method morphs hard problems into routine ones and typically requires no more than high school math. (The complete solution to 2a2+3b2=5c2 is included in the book.) In addition to equations of degree two, the book addresses degree-three equations—a branch of number theory that is today something of a cottage industry, and these problems translate into “elliptic curves”. This important part of the book includes many pictures along with the exposition, making the material meaningful and easy to grasp. This book will fit nicely into an introductory course on number theory. In addition, the many solved examples, illustrations, and exercises make self-studying the book an option for students, thus becoming a natural candidate for a capstone course.
Book Synopsis Wavelet Analysis and Applications by : Tao Qian
Download or read book Wavelet Analysis and Applications written by Tao Qian and published by Springer Science & Business Media. This book was released on 2007-02-24 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume reflects the latest developments in the area of wavelet analysis and its applications. Since the cornerstone lecture of Yves Meyer presented at the ICM 1990 in Kyoto, to some extent, wavelet analysis has often been said to be mainly an applied area. However, a significant percentage of contributions now are connected to theoretical mathematical areas, and the concept of wavelets continuously stretches across various disciplines of mathematics. Key topics: Approximation and Fourier Analysis Construction of Wavelets and Frame Theory Fractal and Multifractal Theory Wavelets in Numerical Analysis Time-Frequency Analysis Adaptive Representation of Nonlinear and Non-stationary Signals Applications, particularly in image processing Through the broad spectrum, ranging from pure and applied mathematics to real applications, the book will be most useful for researchers, engineers and developers alike.
Book Synopsis Multidimensional Systems Theory and Applications by : N.K. Bose
Download or read book Multidimensional Systems Theory and Applications written by N.K. Bose and published by Springer. This book was released on 2013-12-20 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Second Edition of this book includes an abundance of examples to illustrate advanced concepts and brings out in a text book setting the algorithms for bivariate polynomial matrix factorization results that form the basis of two-dimensional systems theory. Algorithms and their implementation using symbolic algebra are emphasized.
