Modern Trends In Hypercomplex Analysis
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Modern Trends In Hypercomplex Analysis
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Author : Swanhild Bernstein
language : en
Publisher: Birkhäuser
Release Date : 2016-11-21
Modern Trends In Hypercomplex Analysis written by Swanhild Bernstein and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-21 with Mathematics categories.
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.
Current Trends In Analysis Its Applications And Computation
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Author : Paula Cerejeiras
language : en
Publisher: Springer Nature
Release Date : 2022-10-03
Current Trends In Analysis Its Applications And Computation written by Paula Cerejeiras and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-03 with Mathematics categories.
This volume contains the contributions of the participants of the 12th ISAAC congress which was held at the University of Aveiro, Portugal, from July 29 to August 3, 2019. These contributions originate from the following sessions: Applications of dynamical systems theory in biology, Complex Analysis and Partial Differential Equations, Complex Geometry, Complex Variables and Potential Theory, Constructive Methods in the Theory of Composite and Porous Media, Function Spaces and Applications, Generalized Functions and Applications, Geometric & Regularity Properties of Solutions to Elliptic and Parabolic PDEs, Geometries Defined by Differential Forms, Partial Differential Equations on Curved Spacetimes, Partial Differential Equations with Nonstandard Growth, Quaternionic and Clifford Analysis, Recent Progress in Evolution Equations, Wavelet theory and its Related Topics.
Operator Theory For Complex And Hypercomplex Analysis
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Author : Enrique Ramírez de Arellano
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Operator Theory For Complex And Hypercomplex Analysis written by Enrique Ramírez de Arellano and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
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 opertors, convolution operators on Lie groups, pseudodifferential operators, etc. The study of these operators arises from integral representations for different classes of functions, enriches pure opertor 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 and Complex and Hypercomplex Analysis", held in Decenber 1994 in Mexico City.
Advances In Hypercomplex Analysis
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Author : Graziano Gentili
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-14
Advances In Hypercomplex Analysis written by Graziano Gentili and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-14 with Mathematics categories.
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.
Hypercomplex Analysis New Perspectives And Applications
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Author : Swanhild Bernstein
language : en
Publisher: Springer
Release Date : 2014-10-10
Hypercomplex Analysis New Perspectives And Applications written by Swanhild Bernstein and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-10 with Mathematics categories.
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.
Recent Trends In Toeplitz And Pseudodifferential Operators
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Author : Roland V. Duduchava
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-02-04
Recent Trends In Toeplitz And Pseudodifferential Operators written by Roland V. Duduchava and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-04 with Mathematics categories.
The aim of the book is to present new results in operator theory and its applications. In particular, the book is devoted to operators with automorphic symbols, applications of the methods of modern operator theory and differential geometry to some problems of theory of elasticity, quantum mechanics, hyperbolic systems of partial differential equations with multiple characteristics, Laplace-Beltrami operators on manifolds with singular points. Moreover, the book comprises new results in the theory of Wiener-Hopf operators with oscillating symbols, large hermitian Toeplitz band matrices, commutative algebras of Toeplitz operators, and discusses a number of other topics.
Recent Trends In Fractional Calculus And Its Applications
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Author : Praveen Agarwal
language : en
Publisher: Elsevier
Release Date : 2024-07-02
Recent Trends In Fractional Calculus And Its Applications written by Praveen Agarwal and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-02 with Science categories.
Recent Trends in Fractional Calculus and Its Applications addresses the answer to this very basic question: "Why is Fractional Calculus important?" Until recent times, Fractional Calculus was considered as a rather esoteric mathematical theory without applications, but in the last few decades there has been an explosion of research activities on the application of Fractional Calculus to very diverse scientific fields ranging from the physics of diffusion and advection phenomena, to control systems to finance and economics. An important part of mathematical modelling of objects and processes is a description of their dynamics.The term Fractional Calculus is more than 300 years old. It is a generalization of the ordinary differentiation and integration to noninteger (arbitrary) order. The subject is as old as the calculus of differentiation and goes back to times when Leibniz, Gauss, and Newton invented this kind of calculation. Several mathematicians contributed to this subject over the years. People like Liouville, Riemann, and Weyl made major contributions to the theory of Fractional Calculus. In recent decades the field of Fractional Calculus has attracted the interest of researchers in several areas, including mathematics, physics, chemistry, engineering, finance, and social sciences. - Provides the most recent and up-to-date developments in the Fractional Calculus and its application areas - Presents pre-preparation ideas to help researchers/scientists/clinicians face the new challenges in the application of fractional differential equations - Helps researchers and scientists understand the importance of the Fractional Calculus to solve many problems in Biomedical Engineering and applied sciences
Advancements In Complex Analysis
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Author : Daniel Breaz
language : en
Publisher: Springer Nature
Release Date : 2020-05-12
Advancements In Complex Analysis written by Daniel Breaz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-12 with Mathematics categories.
The contributions to this volume are devoted to a discussion of state-of-the-art research and treatment of problems of a wide spectrum of areas in complex analysis ranging from pure to applied and interdisciplinary mathematical research. Topics covered include: holomorphic approximation, hypercomplex analysis, special functions of complex variables, automorphic groups, zeros of the Riemann zeta function, Gaussian multiplicative chaos, non-constant frequency decompositions, minimal kernels, one-component inner functions, power moment problems, complex dynamics, biholomorphic cryptosystems, fermionic and bosonic operators. The book will appeal to graduate students and research mathematicians as well as to physicists, engineers, and scientists, whose work is related to the topics covered.
Regular Functions Of A Quaternionic Variable
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Author : Graziano Gentili
language : en
Publisher: Springer Nature
Release Date : 2022-09-23
Regular Functions Of A Quaternionic Variable written by Graziano Gentili and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-23 with Mathematics categories.
This book surveys the foundations of the theory of slice regular functions over the quaternions, introduced in 2006, and gives an overview of its generalizations and applications. As in the case of other interesting quaternionic function theories, the original motivations were the richness of the theory of holomorphic functions of one complex variable and the fact that quaternions form the only associative real division algebra with a finite dimension n>2. (Slice) regular functions quickly showed particularly appealing features and developed into a full-fledged theory, while finding applications to outstanding problems from other areas of mathematics. For instance, this class of functions includes polynomials and power series. The nature of the zero sets of regular functions is particularly interesting and strictly linked to an articulate algebraic structure, which allows several types of series expansion and the study of singularities. Integral representation formulas enrich the theory and are fundamental to the construction of a noncommutative functional calculus. Regular functions have a particularly nice differential topology and are useful tools for the construction and classification of quaternionic orthogonal complex structures, where they compensate for the scarcity of conformal maps in dimension four. This second, expanded edition additionally covers a new branch of the theory: the study of regular functions whose domains are not axially symmetric. The volume is intended for graduate students and researchers in complex or hypercomplex analysis and geometry, function theory, and functional analysis in general.
Michele Sce S Works In Hypercomplex Analysis
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Author : Fabrizio Colombo
language : en
Publisher: Springer Nature
Release Date : 2020-10-24
Michele Sce S Works In Hypercomplex Analysis written by Fabrizio Colombo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-24 with Mathematics categories.
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.