New Trends in Microlocal Analysis

ISBN-13: 9784431684152 / Angielski / Miękka / 2012 / 242 str.

J. -M Bony; M. Morimoto

Opis

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.

Spis treści

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.

O autorze

Microlocal analysis, analyzing problems on the phase space (the cotangent bundle of the base space), was initiated by M. Sato around 1970. It is still an active area of mathematics with applications to many fields such as real and complex analysis, representation theory, topology, number theory, and mathematical physics. The present volume covers a large variety of new research.