New Trends in Microlocal Analysis

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.

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.