Galois Theories Of Linear Difference Equations An Introduction
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Galois Theories Of Linear Difference Equations An Introduction
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Author : Charlotte Hardouin
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-04-27
Galois Theories Of Linear Difference Equations An Introduction written by Charlotte Hardouin 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 2016-04-27 with Mathematics categories.
This book is a collection of three introductory tutorials coming out of three courses given at the CIMPA Research School “Galois Theory of Difference Equations” in Santa Marta, Columbia, July 23–August 1, 2012. The aim of these tutorials is to introduce the reader to three Galois theories of linear difference equations and their interrelations. Each of the three articles addresses a different galoisian aspect of linear difference equations. The authors motivate and give elementary examples of the basic ideas and techniques, providing the reader with an entry to current research. In addition each article contains an extensive bibliography that includes recent papers; the authors have provided pointers to these articles allowing the interested reader to explore further.
Galois Theory Of Difference Equations
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Author : Marius van der Put
language : en
Publisher: Springer
Release Date : 2006-11-14
Galois Theory Of Difference Equations written by Marius van der Put and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
This book lays the algebraic foundations of a Galois theory of linear difference equations and shows its relationship to the analytic problem of finding meromorphic functions asymptotic to formal solutions of difference equations. Classically, this latter question was attacked by Birkhoff and Tritzinsky and the present work corrects and greatly generalizes their contributions. In addition results are presented concerning the inverse problem in Galois theory, effective computation of Galois groups, algebraic properties of sequences, phenomena in positive characteristics, and q-difference equations. The book is aimed at advanced graduate researchers and researchers.
Symmetries And Integrability Of Difference Equations
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Author : Decio Levi
language : en
Publisher: Springer
Release Date : 2017-06-30
Symmetries And Integrability Of Difference Equations written by Decio Levi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-30 with Science categories.
This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference equations. Difference equations are playing an increasingly important role in the natural sciences. Indeed, many phenomena are inherently discrete and thus naturally described by difference equations. More fundamentally, in subatomic physics, space-time may actually be discrete. Differential equations would then just be approximations of more basic discrete ones. Moreover, when using differential equations to analyze continuous processes, it is often necessary to resort to numerical methods. This always involves a discretization of the differential equations involved, thus replacing them by difference ones. Each of the nine peer-reviewed chapters in this volume serves as a self-contained treatment of a topic, containing introductory material as well as the latest research results and exercises. Each chapter is presented by one or more early career researchers in the specific field of their expertise and, in turn, written for early career researchers. As a survey of the current state of the art, this book will serve as a valuable reference and is particularly well suited as an introduction to the field of symmetries and integrability of difference equations. Therefore, the book will be welcomed by advanced undergraduate and graduate students as well as by more advanced researchers.
Intrinsic Approach To Galois Theory Of Q Difference Equations
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Author : Lucia Di Vizio
language : en
Publisher: American Mathematical Society
Release Date : 2022-08-31
Intrinsic Approach To Galois Theory Of Q Difference Equations written by Lucia Di Vizio and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-31 with Mathematics categories.
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Differential Galois Theory Through Riemann Hilbert Correspondence
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Author : Jacques Sauloy
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-12-07
Differential Galois Theory Through Riemann Hilbert Correspondence written by Jacques Sauloy 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 2016-12-07 with Mathematics categories.
Differential Galois theory is an important, fast developing area which appears more and more in graduate courses since it mixes fundamental objects from many different areas of mathematics in a stimulating context. For a long time, the dominant approach, usually called Picard-Vessiot Theory, was purely algebraic. This approach has been extensively developed and is well covered in the literature. An alternative approach consists in tagging algebraic objects with transcendental information which enriches the understanding and brings not only new points of view but also new solutions. It is very powerful and can be applied in situations where the Picard-Vessiot approach is not easily extended. This book offers a hands-on transcendental approach to differential Galois theory, based on the Riemann-Hilbert correspondence. Along the way, it provides a smooth, down-to-earth introduction to algebraic geometry, category theory and tannakian duality. Since the book studies only complex analytic linear differential equations, the main prerequisites are complex function theory, linear algebra, and an elementary knowledge of groups and of polynomials in many variables. A large variety of examples, exercises, and theoretical constructions, often via explicit computations, offers first-year graduate students an accessible entry into this exciting area.
Basic Modern Theory Of Linear Complex Analytic Q Difference Equations
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Author : Jacques Sauloy
language : en
Publisher: American Mathematical Society
Release Date : 2024-11-06
Basic Modern Theory Of Linear Complex Analytic Q Difference Equations written by Jacques Sauloy and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-06 with Mathematics categories.
The roots of the modern theories of differential and $q$-difference equations go back in part to an article by George D. Birkhoff, published in 1913, dealing with the three ?sister theories? of differential, difference and $q$-difference equations. This book is about $q$-difference equations and focuses on techniques inspired by differential equations, in line with Birkhoff's work, as revived over the last three decades. It follows the approach of the Ramis school, mixing algebraic and analytic methods. While it uses some $q$-calculus and is illustrated by $q$-special functions, these are not its main subjects. After a gentle historical introduction with emphasis on mathematics and a thorough study of basic problems such as elementary $q$-functions, elementary $q$-calculus, and low order equations, a detailed algebraic and analytic study of scalar equations is followed by the usual process of transforming them into systems and back again. The structural algebraic and analytic properties of systems are then described using $q$-difference modules (Newton polygon, filtration by the slopes). The final chapters deal with Fuchsian and irregular equations and systems, including their resolution, classification, Riemann-Hilbert correspondence, and Galois theory. Nine appendices complete the book and aim to help the reader by providing some fundamental yet not universally taught facts. There are 535 exercises of various styles and levels of difficulty. The main prerequisites are general algebra and analysis as taught in the first three years of university. The book will be of interest to expert and non-expert researchers as well as graduate students in mathematics and physics.
Algebraic Theory Of Differential Equations
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Author :
language : en
Publisher: Cambridge University Press
Release Date :
Algebraic Theory Of Differential Equations written by and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Transcendence In Algebra Combinatorics Geometry And Number Theory
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Author : Alin Bostan
language : en
Publisher: Springer Nature
Release Date : 2021-11-02
Transcendence In Algebra Combinatorics Geometry And Number Theory written by Alin Bostan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-02 with Mathematics categories.
This proceedings volume gathers together original articles and survey works that originate from presentations given at the conference Transient Transcendence in Transylvania, held in Brașov, Romania, from May 13th to 17th, 2019. The conference gathered international experts from various fields of mathematics and computer science, with diverse interests and viewpoints on transcendence. The covered topics are related to algebraic and transcendental aspects of special functions and special numbers arising in algebra, combinatorics, geometry and number theory. Besides contributions on key topics from invited speakers, this volume also brings selected papers from attendees.
Anti Differentiation And The Calculation Of Feynman Amplitudes
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Author : Johannes Blümlein
language : en
Publisher: Springer Nature
Release Date : 2021-11-26
Anti Differentiation And The Calculation Of Feynman Amplitudes written by Johannes Blümlein and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-26 with Science categories.
This volume comprises review papers presented at the Conference on Antidifferentiation and the Calculation of Feynman Amplitudes, held in Zeuthen, Germany, in October 2020, and a few additional invited reviews. The book aims at comprehensive surveys and new innovative results of the analytic integration methods of Feynman integrals in quantum field theory. These methods are closely related to the field of special functions and their function spaces, the theory of differential equations and summation theory. Almost all of these algorithms have a strong basis in computer algebra. The solution of the corresponding problems are connected to the analytic management of large data in the range of Giga- to Terabytes. The methods are widely applicable to quite a series of other branches of mathematics and theoretical physics.
Jordan Structures In Lie Algebras
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Author : Antonio Fernández López
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-08-19
Jordan Structures In Lie Algebras written by Antonio Fernández López 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 2019-08-19 with Mathematics categories.
Explores applications of Jordan theory to the theory of Lie algebras. After presenting the general theory of nonassociative algebras and of Lie algebras, the book then explains how properties of the Jordan algebra attached to a Jordan element of a Lie algebra can be used to reveal properties of the Lie algebra itself.