## New trends in microlocal analysisMicrolocal 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. |

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### Contents

Fourier Integral Operators and WeylHormander Calculus | 3 |

The Wick calculus of pseudodifferential operatros and energy estimates | 23 |

Eigen functions of the Laplacian of exponential type | 39 |

Copyright | |

5 other sections not shown

### Common terms and phrases

algebra algorithm assume belongs Besov spaces boundary value calculation Cauchy problem characteristic variety codimension coefficients cohomology complex computation conic neighborhood conic neighbourhood consider constant coordinate Corollary D-modules defined Definition denote differential operators elementary solution elliptic exists finite formula Fourier integral operators Fourier transform Fourier-Borel transformation function spaces Grobner basis Hence holomorphic functions holonomic system hyperfunction implies inequality initial data inverse isomorphism Kashiwara Kawai kernel Lame equation Lemma linear Lp(dx manifold Math Mathematics microdifferential operators microfunctions microlocal analysis module morphism Morrey spaces Navier-Stokes equation neighborhood norm obtain open convex Painleve equations Phys polynomial principal symbol Proposition prove pseudo-differential operators quantization Radon measures real analytic Remark resp satisfies the condition self-similar sheaf sheaves singularities solvability stationary solution Stokes submanifold subset sufficiently small symplectic tempered theory uniformly confined unique Univ vanishes Weyl Weyl quantization zero