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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.

Singularities of integrals

2011-04-22 Mathematics
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Release : 2011-04-22
Genre : Mathematics
Kind : eBook
Book Rating : 035/5 ( reviews)

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Book Synopsis Singularities of integrals by : Frédéric Pham

Download or read book Singularities of integrals written by Frédéric Pham. This book was released on 2011-04-22. Available in PDF, EPUB and Kindle. Book excerpt: Bringing together two fundamental texts from Frédéric Pham’s research on singular integrals, the first part of this book focuses on topological and geometrical aspects while the second explains the analytic approach. Using notions developed by J. Leray in the calculus of residues in several variables and R. Thom’s isotopy theorems, Frédéric Pham’s foundational study of the singularities of integrals lies at the interface between analysis and algebraic geometry, culminating in the Picard-Lefschetz formulae. These mathematical structures, enriched by the work of Nilsson, are then approached using methods from the theory of differential equations and generalized from the point of view of hyperfunction theory and microlocal analysis. Providing a ‘must-have’ introduction to the singularities of integrals, a number of supplementary references also offer a convenient guide to the subjects covered. This book will appeal to both mathematicians and physicists with an interest in the area of singularities of integrals. Frédéric Pham, now retired, was Professor at the University of Nice. He has published several educational and research texts. His recent work concerns semi-classical analysis and resurgent functions.

Mixed Automorphic Forms, Torus Bundles, and Jacobi Forms

2004-05-13 Computers
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Release : 2004-05-13
Genre : Computers
Kind : eBook
Book Rating : 224/5 ( reviews)

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Book Synopsis Mixed Automorphic Forms, Torus Bundles, and Jacobi Forms by : Min Ho Lee

Download or read book Mixed Automorphic Forms, Torus Bundles, and Jacobi Forms written by Min Ho Lee. This book was released on 2004-05-13. Available in PDF, EPUB and Kindle. Book excerpt: This volume deals with various topics around equivariant holomorphic maps of Hermitian symmetric domains and is intended for specialists in number theory and algebraic geometry. In particular, it contains a comprehensive exposition of mixed automorphic forms that has never yet appeared in book form. The main goal is to explore connections among complex torus bundles, mixed automorphic forms, and Jacobi forms associated to an equivariant holomorphic map. Both number-theoretic and algebro-geometric aspects of such connections and related topics are discussed.

The Art of Random Walks

2006-05-17 Mathematics
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Release : 2006-05-17
Genre : Mathematics
Kind : eBook
Book Rating : 275/5 ( reviews)

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Book Synopsis The Art of Random Walks by : Andras Telcs

Download or read book The Art of Random Walks written by Andras Telcs. This book was released on 2006-05-17. Available in PDF, EPUB and Kindle. Book excerpt: Einstein proved that the mean square displacement of Brownian motion is proportional to time. He also proved that the diffusion constant depends on the mass and on the conductivity (sometimes referred to Einstein’s relation). The main aim of this book is to reveal similar connections between the physical and geometric properties of space and diffusion. This is done in the context of random walks in the absence of algebraic structure, local or global spatial symmetry or self-similarity. The author studies the heat diffusion at this general level and discusses the following topics: The multiplicative Einstein relation, Isoperimetric inequalities, Heat kernel estimates Elliptic and parabolic Harnack inequality.

Asymptotics for Dissipative Nonlinear Equations

2006-04-21 Mathematics
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Release : 2006-04-21
Genre : Mathematics
Kind : eBook
Book Rating : 598/5 ( reviews)

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Book Synopsis Asymptotics for Dissipative Nonlinear Equations by : Nakao Hayashi

Download or read book Asymptotics for Dissipative Nonlinear Equations written by Nakao Hayashi. This book was released on 2006-04-21. Available in PDF, EPUB and Kindle. Book excerpt: Many of problems of the natural sciences lead to nonlinear partial differential equations. However, only a few of them have succeeded in being solved explicitly. Therefore different methods of qualitative analysis such as the asymptotic methods play a very important role. This is the first book in the world literature giving a systematic development of a general asymptotic theory for nonlinear partial differential equations with dissipation. Many typical well-known equations are considered as examples, such as: nonlinear heat equation, KdVB equation, nonlinear damped wave equation, Landau-Ginzburg equation, Sobolev type equations, systems of equations of Boussinesq, Navier-Stokes and others.

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