Abstract
CONTENTS Introduction §1. Technical preliminaries 1. Symplectic and contact geometry 2. Integral calculus on 3. Homogeneous and formally homogeneous generalized functions on §2. Fourier transforms of homogeneous functions 1. Statement of the problem 2. The main lemma 3. Structure theorem for the Fourier transform of a homogeneous function 4. Commutation formulae and the choice of constants §3. Fourier-Maslov integral operators 1. The Maslov canonical operator 2. Fourier-Maslov integral operators §4. Examples and applications 1. Preliminary remarks 2. The discontinuity propagation problem 3. The discontinuity metamorphosis problem 4. Investigation of Green's function of the Cauchy problem §5. Microlocal classification of pseudodifferential operators 1. Microlocal equivalence 2. Elliptic operators and operators of principal type 3. Operators of subprincipal type §6. Equations of principal and subprincipal types 1. Equations of principal type 2. Proof of Theorem 1 3. Equations of subprincipal type References
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