Basic Modern Theory of Linear Complex Analytic $q$-Difference Equations: 287 (Mathematical Surveys and Monographs) - Softcover
Synopsis
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.
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Basic Modern Theory of Linear Complex Analytic $q$-Difference Equations (eng)
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Basic Modern Theory of Linear Complex Analytic $q$-Difference Equations: 287 (Mathematical Surveys and Monographs)
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ISBN 13: 9781470478407
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Basic Modern Theory of Linear Complex Analytic $q$-Difference Equations (Paperback)
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ISBN 13: 9781470478407
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Paperback. Condition: new. Paperback. 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. Based on early ideas by Birkhoff, this work reexamines q-difference equations through a fusion of algebraic and analytic methods. It moves from elementary q-calculus and scalar challenges to transforming systems, ultimately addressing Fuchsian versus irregular cases with Riemann-Hilbert and Galois theory. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9781470478407
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Basic Modern Theory of Linear Complex Analytic $q$-Difference Equations
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ISBN 10: 1470478404
ISBN 13: 9781470478407
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Paperback. Condition: New. 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. Seller Inventory # LU-9781470478407
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Basic Modern Theory of Linear Complex Analytic $q$-Difference Equations: 287 (Mathematical Surveys and Monographs)
Published by
American Mathematical Society, 2024
ISBN 10: 1470478404
ISBN 13: 9781470478407
New
Softcover
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Condition: New. 2024. paperback. . . . . . Books ship from the US and Ireland. Seller Inventory # V9781470478407
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Basic Modern Theory of Linear Complex Analytic $q$-Difference Equations
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Basic Modern Theory of Linear Complex Analytic $q$-Difference Equations (Mathematical Surveys and Monographs)
Published by
American Mathematical Society, 2024
ISBN 10: 1470478404
ISBN 13: 9781470478407
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Softcover
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Basic Modern Theory of Linear Complex Analytic $q$-Difference Equations
Published by
American Mathematical Society, US, 2024
ISBN 10: 1470478404
ISBN 13: 9781470478407
New
Paperback
Seller: Rarewaves.com UK, London, United Kingdom
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Paperback. Condition: New. 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. Seller Inventory # LU-9781470478407
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