Application Of Holomorphic Functions In Two And Higher Dimensions

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Application of Holomorphic Functions in Two and Higher Dimensions

Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig
Application of Holomorphic Functions in Two and Higher Dimensions Book PDF

Author : Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig
Publisher : Springer
Page : 390 pages
File Size : 51,9 Mb
Release : 2016-06-20
Category : Mathematics
ISBN : 9783034809641

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Application of Holomorphic Functions in Two and Higher Dimensions by Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig Pdf

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 Throughout the book the authors endeavor to present historical references and important personalities.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.

Applied Analysis, Optimization and Soft Computing

Tanmoy Som,Debdas Ghosh,Oscar Castillo,Adrian Petrusel,Dayaram Sahu
Applied Analysis Optimization and Soft Computing Book PDF

Author : Tanmoy Som,Debdas Ghosh,Oscar Castillo,Adrian Petrusel,Dayaram Sahu
Publisher : Springer Nature
Page : 425 pages
File Size : 43,9 Mb
Release : 2023-06-10
Category : Mathematics
ISBN : 9789819905973

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Applied Analysis, Optimization and Soft Computing by Tanmoy Som,Debdas Ghosh,Oscar Castillo,Adrian Petrusel,Dayaram Sahu Pdf

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

Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig
Holomorphic Functions in the Plane and n dimensional Space Book PDF

Author : Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig
Publisher : Springer Science & Business Media
Page : 407 pages
File Size : 55,9 Mb
Release : 2007-11-16
Category : Mathematics
ISBN : 9783764382711

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Holomorphic Functions in the Plane and n-dimensional Space by Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig Pdf

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

Andreas Defant,Domingo García,Manuel Maestre,Pablo Sevilla-Peris
Dirichlet Series and Holomorphic Functions in High Dimensions Book PDF

Author : Andreas Defant,Domingo García,Manuel Maestre,Pablo Sevilla-Peris
Publisher : Cambridge University Press
Page : 709 pages
File Size : 55,8 Mb
Release : 2019-08-08
Category : Mathematics
ISBN : 9781108476713

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Dirichlet Series and Holomorphic Functions in High Dimensions by Andreas Defant,Domingo García,Manuel Maestre,Pablo Sevilla-Peris Pdf

Using contemporary concepts, this book describes the interaction between Dirichlet series and holomorphic functions in high dimensions.

Quadrature Domains and Their Applications

Harold S. Shapiro
Quadrature Domains and Their Applications Book PDF

Author : Harold S. Shapiro
Publisher : Springer Science & Business Media
Page : 312 pages
File Size : 48,8 Mb
Release : 2005-01-27
Category : Mathematics
ISBN : 3764371455

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Quadrature Domains and Their Applications by Harold S. Shapiro Pdf

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

Eberhard Lanckau,Wolfgang Tutschke
Complex Analysis Methods Trends and Applications Book PDF

Author : Eberhard Lanckau,Wolfgang Tutschke
Publisher : Walter de Gruyter GmbH & Co KG
Page : 400 pages
File Size : 51,6 Mb
Release : 1983-12-31
Category : Mathematics
ISBN : 9783112707753

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Complex Analysis – Methods, Trends, and Applications by Eberhard Lanckau,Wolfgang Tutschke Pdf

No detailed description available for "Complex Analysis – Methods, Trends, and Applications".

Geometric Function Theory in One and Higher Dimensions

Ian Graham
Geometric Function Theory in One and Higher Dimensions Book PDF

Author : Ian Graham
Publisher : CRC Press
Page : 572 pages
File Size : 42,9 Mb
Release : 2003-03-18
Category : Mathematics
ISBN : 0203911628

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Geometric Function Theory in One and Higher Dimensions by Ian Graham Pdf

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

Encyclopaedia of Mathematics

Michiel Hazewinkel
Encyclopaedia of Mathematics Book PDF

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 595 pages
File Size : 52,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401512886

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Encyclopaedia of Mathematics by Michiel Hazewinkel Pdf

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.

Holomorphic Functions and Integral Representations in Several Complex Variables

R. Michael Range
Holomorphic Functions and Integral Representations in Several Complex Variables Book PDF

Author : R. Michael Range
Publisher : Springer Science & Business Media
Page : 405 pages
File Size : 46,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475719185

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Holomorphic Functions and Integral Representations in Several Complex Variables by R. Michael Range Pdf

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.

Theory Of Complex Variable

R.K. Pandey
Theory Of Complex Variable Book PDF

Author : R.K. Pandey
Publisher : Discovery Publishing House
Page : 354 pages
File Size : 41,8 Mb
Release : 2007
Category : Functions of complex variables
ISBN : 8183562957

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Theory Of Complex Variable by R.K. Pandey Pdf

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.

Integral Methods in Science and Engineering, Volume 1

Christian Constanda,Matteo Dalla Riva,Pier Domenico Lamberti,Paolo Musolino
Integral Methods in Science and Engineering Volume 1 Book PDF

Author : Christian Constanda,Matteo Dalla Riva,Pier Domenico Lamberti,Paolo Musolino
Publisher : Birkhäuser
Page : 340 pages
File Size : 43,7 Mb
Release : 2017-09-08
Category : Mathematics
ISBN : 9783319593845

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Integral Methods in Science and Engineering, Volume 1 by Christian Constanda,Matteo Dalla Riva,Pier Domenico Lamberti,Paolo Musolino Pdf

This contributed volume contains a collection of articles on the most recent advances in integral methods. The first of two volumes, this work focuses on the construction of theoretical integral methods. Written by internationally recognized researchers, the chapters in this book are based on talks given at the Fourteenth International Conference on Integral Methods in Science and Engineering, held July 25-29, 2016, in Padova, Italy. A broad range of topics is addressed, such as:• Integral equations• Homogenization• Duality methods• Optimal design• Conformal techniques This collection will be of interest to researchers in applied mathematics, physics, and mechanical and electrical engineering, as well as graduate students in these disciplines, and to other professionals who use integration as an essential tool in their work.

An Introduction to Multicomplex SPates and Functions

Price
An Introduction to Multicomplex SPates and Functions Book PDF

Author : Price
Publisher : Routledge
Page : 196 pages
File Size : 48,8 Mb
Release : 2018-05-11
Category : Mathematics
ISBN : 9781351467087

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An Introduction to Multicomplex SPates and Functions by Price Pdf

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

Wavelet Analysis and Applications

Tao Qian,Mang I. Vai,Yuesheng Xu
Wavelet Analysis and Applications Book PDF

Author : Tao Qian,Mang I. Vai,Yuesheng Xu
Publisher : Springer Science & Business Media
Page : 574 pages
File Size : 55,5 Mb
Release : 2007-02-24
Category : Mathematics
ISBN : 9783764377786

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Wavelet Analysis and Applications by Tao Qian,Mang I. Vai,Yuesheng Xu Pdf

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.

A Gateway to Number Theory: Applying the Power of Algebraic Curves

Keith Kendig
A Gateway to Number Theory Applying the Power of Algebraic Curves Book PDF

Author : Keith Kendig
Publisher : American Mathematical Soc.
Page : 207 pages
File Size : 50,8 Mb
Release : 2021-04-23
Category : Education
ISBN : 9781470456221

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A Gateway to Number Theory: Applying the Power of Algebraic Curves by Keith Kendig Pdf

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.

Spaces of Holomorphic Functions in the Unit Ball

Kehe Zhu
Spaces of Holomorphic Functions in the Unit Ball Book PDF

Author : Kehe Zhu
Publisher : Springer Science & Business Media
Page : 281 pages
File Size : 43,8 Mb
Release : 2006-03-22
Category : Mathematics
ISBN : 9780387275390

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Spaces of Holomorphic Functions in the Unit Ball by Kehe Zhu Pdf

Can be used as a graduate text Contains many exercises Contains new results