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Author : Sorin G. Gal
Publisher : Nova Publishers
Page : 340 pages
File Size : 48,7 Mb
Release : 2002
Category : Mathematics
ISBN : 1590333640
Introduction to Geometric Function Theory of Hypercomplex Variables
Author : Enrique Ramírez de Arellano,N. Salinas,M. V. Shapiro,N. L. Vasilevski
Publisher : American Mathematical Soc.
Page : 298 pages
File Size : 41,7 Mb
Release : 1998
Category : Mathematics
ISBN : 9780821806777
This book presents a collection of papers on certain aspects of general operator theory related to classes of important operators: singular integral, Toeplitz and Bergman operators, convolution operators on Lie groups, pseudodifferential operators, etc. The study of these operators arises from integral representations for different classes of functions, enriches pure operator theory, and is influential and beneficial for important areas of analysis. Particular attention is paid to the fruitful interplay of recent developments of complex and hypercomplex analysis on one side and to operator theory on the other. The majority of papers illustrate this interplay as well as related applications. The papers represent the proceedings of the conference ``Operator Theory for Complex and Hypercomplex Analysis'', held in December 1994 in Mexico City.
Author : Yu.M. Berezansky,A.A. Kalyuzhnyi
Publisher : Springer Science & Business Media
Page : 494 pages
File Size : 55,6 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9789401717588
First works related to the topics covered in this book belong to J. Delsarte and B. M. Le vitan and appeared since 1938. In these works, the families of operators that generalize usual translation operators were investigated and the corresponding harmonic analysis was constructed. Later, starting from 1950, it was noticed that, in such constructions, an important role is played by the fact that the kernels of the corresponding convolutions of functions are nonnegative and by the properties of the normed algebras generated by these convolutions. That was the way the notion of hypercomplex system with continu ous basis appeared. A hypercomplex system is a normed algebra of functions on a locally compact space Q-the "basis" of this hypercomplex system. Later, similar objects, hypergroups, were introduced, which have complex-valued measures on Q as elements and convolution defined to be essentially the convolution of functionals and dual to the original convolution (if measures are regarded as functionals on the space of continuous functions on Q). However, until 1991, the time when this book was written in Russian, there were no monographs containing fundamentals of the theory (with an exception of a short section in the book by Yu. M. Berezansky and Yu. G. Kondratiev [BeKo]). The authors wanted to give an introduction to the theory and cover the most important subsequent results and examples.
Author : Swanhild Bernstein,Uwe Kähler,Irene Sabadini,Frank Sommen
Publisher : Springer
Page : 227 pages
File Size : 46,5 Mb
Release : 2014-10-10
Category : Mathematics
ISBN : 9783319087719
Hypercomplex analysis is the extension of complex analysis to higher dimensions where the concept of a holomorphic function is substituted by the concept of a monogenic function. In recent decades this theory has come to the forefront of higher dimensional analysis. There are several approaches to this: quaternionic analysis which merely uses quaternions, Clifford analysis which relies on Clifford algebras, and generalizations of complex variables to higher dimensions such as split-complex variables. This book includes a selection of papers presented at the session on quaternionic and hypercomplex analysis at the ISAAC conference 2013 in Krakow, Poland. The topics covered represent new perspectives and current trends in hypercomplex analysis and applications to mathematical physics, image analysis and processing, and mechanics.
Author : Graziano Gentili,Irene Sabadini,Michael Shapiro,Franciscus Sommen,Daniele C. Struppa
Publisher : Springer Science & Business Media
Page : 149 pages
File Size : 41,9 Mb
Release : 2012-11-14
Category : Mathematics
ISBN : 9788847024458
This volume is intended to collect important research results to the lectures and discussions which took Place in Rome, at the INdAM Workshop on Different Notions of Regularity for Functions of Quaternionic Variables in September 2010. This volume will collect recent and new results, which are connected to the topic covered during the workshop. The work aims at bringing together international leading specialists in the field of Quaternionic and Clifford Analysis, as well as young researchers interested in the subject, with the idea of presenting and discussing recent results, analyzing new trends and techniques in the area and, in general, of promoting scientific collaboration. Particular attention is paid to the presentation of different notions of regularity for functions of hypercomplex variables, and to the study of the main features of the theories that they originate.
Author : Irene Sabadini,Michael Shapiro,Franciscus Sommen
Publisher : Springer Science & Business Media
Page : 289 pages
File Size : 48,9 Mb
Release : 2009-04-21
Category : Mathematics
ISBN : 9783764398934
Contains selected papers from the ISAAC conference 2007 and invited contributions. This book covers various topics that represent the main streams of research in hypercomplex analysis as well as the expository articles. It is suitable for researchers and postgraduate students in various areas of mathematical analysis.
Author : Swanhild Bernstein,Uwe Kähler,Irene Sabadini,Franciscus Sommen
Publisher : Birkhäuser
Page : 310 pages
File Size : 52,9 Mb
Release : 2016-11-21
Category : Mathematics
ISBN : 9783319425290
This book contains a selection of papers presented at the session "Quaternionic and Clifford Analysis" at the 10th ISAAC Congress held in Macau in August 2015. The covered topics represent the state-of-the-art as well as new trends in hypercomplex analysis and its applications.
Author : Fabrizio Colombo,Irene Sabadini,Daniele C. Struppa
Publisher : Springer Nature
Page : 126 pages
File Size : 49,6 Mb
Release : 2020-10-24
Category : Mathematics
ISBN : 9783030502164
This book presents English translations of Michele Sce’s most important works, originally written in Italian during the period 1955-1973, on hypercomplex analysis and algebras of hypercomplex numbers. Despite their importance, these works are not very well known in the mathematics community because of the language they were published in. Possibly the most remarkable instance is the so-called Fueter-Sce mapping theorem, which is a cornerstone of modern hypercomplex analysis, and is not yet understood in its full generality. This volume is dedicated to revealing and describing the framework Sce worked in, at an exciting time when the various generalizations of complex analysis in one variable were still in their infancy. In addition to faithfully translating Sce’s papers, the authors discuss their significance and explain their connections to contemporary research in hypercomplex analysis. They also discuss many concrete examples that can serve as a basis for further research. The vast majority of the results presented here will be new to readers, allowing them to finally access the original sources with the benefit of comments from fellow mathematicians active in the field of hypercomplex analysis. As such, the book offers not only an important chapter in the history of hypercomplex analysis, but also a roadmap for further exciting research in the field.
Author : Heinrich Begehr,R.P. Gilbert,Wen-Chung Guo
Publisher : Springer Science & Business Media
Page : 367 pages
File Size : 54,8 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461332763
This volume of the Proceedings of the congress ISAAC '97 collects the con tributions of the four sections 1. Function theoretic and functional analytic methods for pde, 2. Applications of function theory of several complex variables to pde, 3. Integral equations and boundary value problems, 4. Partial differential equations. Most but not all of the authors have participated in the congress. Unfortunately some from Eastern Europe and Asia have not managed to come because of lack of financial support. Nevertheless their manuscripts of the proposed talks are included in this volume. The majority of the papers deal with complex methods. Among them boundary value problems in particular the Riemann-Hilbert, the Riemann (Hilbert) and related problems are treated. Boundary behaviour of vector-valued functions are studied too. The Riemann-Hilbert problem is solved for elliptic complex equations, for mixed complex equations, and for several complex variables. It is considered in a general topological setting for mappings into q;n and related to Toeplitz operators. Convolution operators are investigated for nilpotent Lie groups leading to some consequences for the null space of the tangential Cauchy Riemann operator. Some boundary value problems for overdetermined systems in balls of q;n are solved explicitly. A survey is given for the Gauss-Manin connection associated with deformations of curve singularities. Several papers deal with generalizations of analytic functions with various applications to mathematical physics. Singular integrals in quaternionic anal ysis are studied which are applied to the time-harmonic Maxwell equations.
Author : Irene Sabadini,Franciscus Sommen
Publisher : Springer Science & Business Media
Page : 284 pages
File Size : 41,8 Mb
Release : 2010-12-21
Category : Mathematics
ISBN : 9783034602464
The purpose of the volume is to bring forward recent trends of research in hypercomplex analysis. The list of contributors includes first rate mathematicians and young researchers working on several different aspects in quaternionic and Clifford analysis. Besides original research papers, there are papers providing the state-of-the-art of a specific topic, sometimes containing interdisciplinary fields. The intended audience includes researchers, PhD students, postgraduate students who are interested in the field and in possible connection between hypercomplex analysis and other disciplines, including mathematical analysis, mathematical physics, algebra.
Author : Alexey Karapetyants,Vladislav Kravchenko,Elijah Liflyand
Publisher : Springer Nature
Page : 475 pages
File Size : 52,5 Mb
Release : 2019-08-28
Category : Mathematics
ISBN : 9783030267483
This proceedings volume gathers selected, peer-reviewed papers from the "Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis VIII" (OTHA 2018) conference, which was held in Rostov-on-Don, Russia, in April 2018. The book covers a diverse range of topics in advanced mathematics, including harmonic analysis, functional analysis, operator theory, function theory, differential equations and fractional analysis – all fields that have been intensively developed in recent decades. Direct and inverse problems arising in mathematical physics are studied and new methods for solving them are presented. Complex multiparameter objects that require the involvement of operators with variable parameters and functional spaces, with fractional and even variable exponents, make these approaches all the more relevant. Given its scope, the book will especially benefit researchers with an interest in new trends in harmonic analysis and operator theory, though it will also appeal to graduate students seeking new and intriguing topics for further investigation.
Author : Yo-Sung Ho
Publisher : Springer
Page : 407 pages
File Size : 54,8 Mb
Release : 2011-11-21
Category : Computers
ISBN : 9783642253461
The two-volume proceedings LNCS 7087 + 7088 constitute the proceedings of the 5th Pacific Rim Symposium, PSIVT 2011, held in Gwangju, Korea, in November 2011. The total of 71 revised papers was carefully reviewed and selected from 168 submissions. The topics covered are: image/video coding and transmission; image/video processing and analysis; imaging and graphics hardware and visualization; image/video retrieval and scene understanding; biomedical image processing and analysis; biometrics and image forensics; and computer vision applications.
Author : Dmitry I. Ignatov,Mikhail Yu. Khachay,Valeri G. Labunets,Natalia Loukachevitch,Sergey I. Nikolenko,Alexander Panchenko,Andrey V. Savchenko,Konstantin Vorontsov
Publisher : Springer
Page : 386 pages
File Size : 48,6 Mb
Release : 2017-02-15
Category : Computers
ISBN : 9783319529202
This book constitutes the proceedings of the 5th International Conference on Analysis of Images, Social Networks and Texts, AIST 2016, held in Yekaterinburg, Russia, in April 2016. The 23 full papers, 7 short papers, and 3 industrial papers were carefully reviewed and selected from 142 submissions. The papers are organized in topical sections on machine learning and data analysis; social networks; natural language processing; analysis of images and video.
Author : Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig
Publisher : Springer
Page : 390 pages
File Size : 52,5 Mb
Release : 2016-06-20
Category : Mathematics
ISBN : 9783034809641
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.
Author : Gürlebeck,Sprössig
Publisher : Birkhäuser
Page : 252 pages
File Size : 50,8 Mb
Release : 2013-03-08
Category : Science
ISBN : 9783034872959