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Fundamentals of Algebraic Microlocal Analysis

2020-08-11 Mathematics
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Release : 2020-08-11
Genre : Mathematics
Kind : eBook
Book Rating : 180/5 ( reviews)

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Book Synopsis Fundamentals of Algebraic Microlocal Analysis by : Goro Kato

Download or read book Fundamentals of Algebraic Microlocal Analysis written by Goro Kato. This book was released on 2020-08-11. Available in PDF, EPUB and Kindle. Book excerpt: "Provides a thorough introduction to the algebraic theory of systems of differential equations, as developed by the Japanese school of M. Sato and his colleagues. Features a complete review of hyperfunction-microfunction theory and the theory of D-modules. Strikes the perfect balance between analytic and algebraic aspects."

Foundations of Algebraic Analysis

1986 Mathematics
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Release : 1986
Genre : Mathematics
Kind : eBook
Book Rating : 138/5 ( reviews)

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Book Synopsis Foundations of Algebraic Analysis by : Masaki Kashiwara

Download or read book Foundations of Algebraic Analysis written by Masaki Kashiwara. This book was released on 1986. Available in PDF, EPUB and Kindle. Book excerpt: The use of algebraic methods for studying analysts is an important theme in modern mathematics. The most significant development in this field is microlocal analysis, that is, the local study of differential equations on cotangent bundles. This treatise provides a thorough description of microlocal analysis starting from its foundations. The book begins with the definition of a hyperfunction. It then carefully develops the microfunction theory and its applications to differential equations and theoretical physics. It also provides a description of microdifferential equations, the microlocalization of linear differential equations. Finally, the authors present the structure theorems for systems of microdifferential equations, where the quantized contact transformations are used as a fundamental device. The microfunction theory, together with the quantized contact transformation theory, constitutes a valuable new viewpoint in linear partial differential equations. Originally published in 1986. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Classical Microlocal Analysis in the Space of Hyperfunctions

2007-05-06 Mathematics
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Release : 2007-05-06
Genre : Mathematics
Kind : eBook
Book Rating : 617/5 ( reviews)

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Book Synopsis Classical Microlocal Analysis in the Space of Hyperfunctions by : Seiichiro Wakabayashi

Download or read book Classical Microlocal Analysis in the Space of Hyperfunctions written by Seiichiro Wakabayashi. This book was released on 2007-05-06. Available in PDF, EPUB and Kindle. Book excerpt: The book develops "Classical Microlocal Analysis" in the spaces of hyperfunctions and microfunctions, which makes it possible to apply the methods in the distribution category to the studies on partial differential equations in the hyperfunction category. Here "Classical Microlocal Analysis" means that it does not use "Algebraic Analysis." The main tool in the text is, in some sense, integration by parts. The studies on microlocal uniqueness, analytic hypoellipticity and local solvability are reduced to the problems to derive energy estimates (or a priori estimates). The author assumes basic understanding of theory of pseudodifferential operators in the distribution category.

Fundamentals of Advanced Mathematics V2

2018-02-03 Mathematics
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Release : 2018-02-03
Genre : Mathematics
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Book Rating : 855/5 ( reviews)

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Book Synopsis Fundamentals of Advanced Mathematics V2 by : Henri Bourles

Download or read book Fundamentals of Advanced Mathematics V2 written by Henri Bourles. This book was released on 2018-02-03. Available in PDF, EPUB and Kindle. Book excerpt: The three volumes of this series of books, of which this is the second, put forward the mathematical elements that make up the foundations of a number of contemporary scientific methods: modern theory on systems, physics and engineering. Whereas the first volume focused on the formal conditions for systems of linear equations (in particular of linear differential equations) to have solutions, this book presents the approaches to finding solutions to polynomial equations and to systems of linear differential equations with varying coefficients. Fundamentals of Advanced Mathematics, Volume 2: Field Extensions, Topology and Topological Vector Spaces, Functional Spaces, and Sheaves begins with the classical Galois theory and the theory of transcendental field extensions. Next, the differential side of these theories is treated, including the differential Galois theory (Picard-Vessiot theory of systems of linear differential equations with time-varying coefficients) and differentially transcendental field extensions. The treatment of analysis includes topology (using both filters and nets), topological vector spaces (using the notion of disked space, which simplifies the theory of duality), and the radon measure (assuming that the usual theory of measure and integration is known). In addition, the theory of sheaves is developed with application to the theory of distributions and the theory of hyperfunctions (assuming that the usual theory of functions of the complex variable is known). This volume is the prerequisite to the study of linear systems with time-varying coefficients from the point-of-view of algebraic analysis and the algebraic theory of nonlinear systems. Present Galois Theory, transcendental field extensions, and Picard Includes sections on Vessiot theory, differentially transcendental field extensions, topology, topological vector spaces, Radon measure, differential calculus in Banach spaces, sheaves, distributions, hyperfunctions, algebraic analysis, and local analysis of systems of linear differential equations

Advances in Microlocal and Time-Frequency Analysis

2020-03-03 Mathematics
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Release : 2020-03-03
Genre : Mathematics
Kind : eBook
Book Rating : 381/5 ( reviews)

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Book Synopsis Advances in Microlocal and Time-Frequency Analysis by : Paolo Boggiatto

Download or read book Advances in Microlocal and Time-Frequency Analysis written by Paolo Boggiatto. This book was released on 2020-03-03. Available in PDF, EPUB and Kindle. Book excerpt: The present volume gathers contributions to the conference Microlocal and Time-Frequency Analysis 2018 (MLTFA18), which was held at Torino University from the 2nd to the 6th of July 2018. The event was organized in honor of Professor Luigi Rodino on the occasion of his 70th birthday. The conference’s focus and the contents of the papers reflect Luigi’s various research interests in the course of his long and extremely prolific career at Torino University.

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