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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.
CONTENTS: J.M. Bony: Analyse microlocale des equations aux derivees
partielles non lineaires.- G.G. Grubb: Parabolic
pseudo-differential boundary problems and applications.- L.
H-rmander: Quadratic hyperbolic operators.- H. Komatsu: Microlocal
analysis in Gevrey classes and in complex domains.- J. Sj-strand:
Microlocal analysis for the periodic magnetic Schr-dinger equation
and related questions.
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