Contact Geometry and Linear Differential Equations

✍ Scribed by Vladimir E. Nazaikinskii; Victor E. Shatalov; Boris Yu. Sternin

• Publisher: De Gruyter
• Year: 1992
• Tongue: English
• Leaves: 228
• Series: De Gruyter Expositions in Mathematics; 6
• Category: Library

✦ Table of Contents

Introduction
Chapter I Homogeneous functions, Fourier transformation, and contact structures
1. Integration on manifolds
2. Analysis on RPn and smooth homogeneous functions on Rn+1
3. Homogeneous and formally homogeneous distributions
4. Fourier transformation of homogeneous functions
5. Homogeneous symplectic and contact structures
6. Functorial properties of the phase space and local representation of Lagrangian manifolds. The classification lemma
Chapter II Fourier-Maslov operators
1. Maslov’s canonical operator (R-equivariant theory)
2. Fourier-Maslov integral operators
3. Singularities of hyperbolic equations; examples and applications
Chapter III Applications to differential equations
1. Equations of principal type
2. Microlocal classification of pseudodifferential operators
3. Equations of subprincipal type
References
Index