Overview

Microlocal analysis began around 1970 when Mikio Sato, along with coauthors Masaki Kashiwara and Takahiro Kawai, wrote a decisive article on the structure of pseudodifferential equations, thus laying the foundation of D-modules and the singular spectrums of hyperfunctions. The key idea is the analysis of problems on the phase space, i.e., the cotangent bundle of the base space. Microlocal analysis is an active area of mathematical research that has been applied to many fields such as real and complex analysis, representation theory, topology, number theory, and mathematical physics. This volume contains the presentations given at a seminar jointly organized by the Japan Society for the Promotion of Science and Centre National des Recherches Scientifiques entitled New Trends in Microlocal Analysis. The book is divided into three parts: partial differential equations and mathematical analysis, mathematical physics, and algebraic analysis - D-modules and sheave theory. The large variety of new research that is covered will prove invaluable to students and researchers alike.

Full Product Details

Author:   J.-M. Bony ,  M. Morimoto
Publisher:   Springer Verlag, Japan
Imprint:   Springer Verlag, Japan
Edition:   Softcover reprint of the original 1st ed. 1997
Dimensions:   Width: 15.50cm , Height: 1.30cm , Length: 23.50cm
Weight:   0.391kg
ISBN:  

9784431684152

ISBN 10:   4431684158
Pages:   242
Publication Date:   12 February 2012
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

I. Partial Differential Equations and Mathematical Analysis.- Fourier Integral Operators and Weyl-Hörmander Calculus.- The Wick calculus of pseudo-differential operatros and energy estimates.- Eigen functions of the Laplacian of exponential type.- Wavelet transforms and operators in various function spaces.- Charcteristic Cauchy Problems in the complex domain.- Stokes Operators for microhyperbolic equations.- II. Mathematical Physics.- Instanton-typc formal solutions to the second Painlevé equations with a large parameter.- Pseudodifferential and Fourier integral operators in scattering theory.- On infrared singularities.- The Navier-Stokes equation with distributions as initial data and application to self-similar solutions.- Bloch function in an external electric field and Berry-Buslaev phase.- III. Algebraic Analysis — D-modules and Sheave Theory.- An Application of symbol calculus.- Elliptic boundary value problems in the space of distributions.- On the holonomic character of the elementary solution of a partial differential operator.- Kernel calculus and extension of contact transformations to D-Modules.- Microfunction solutions of holonomic systems with irregular singularities.- Some algorithmic aspects of the P-module theory.- On higher-codimensional boundary value problems.- Kashiwara’s microlocal analysis of the Bergman kernel for domains with corner.

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