Contact Geometry and Linear Differential Equations (Manuels de Linguistique Et Des Sciences de Communication) (Degruyter Expositions in Mathematics)

The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, BrasilWalter D. Neumann, Columbia University, New York, USAMarkus J. Pflaum, University of Colorado, Boulder, USADierk Schleicher, Aix-Marseille Université, FranceKatrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019)Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019)Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019)Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021)Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021) Back Cover......Page 1 Title......Page 2 Copyright......Page 3 Contents......Page 4 Introduction......Page 6 1. Integration on manifolds ......Page 10 2. Analysis on RP^n and smooth homogeneous functions on R_{*}^{n+1] ......Page 20 3. Homogeneous and formally homogeneous distributions ......Page 33 4. Fourier transformation of homogeneous functions ......Page 39 5. Homogeneous symplectic and contact structures ......Page 53 6. Functorial properties of the phase space and local representation of Lagrangian manifolds. The classification lemma ......Page 72 1. Maslov's canonical operator theory) ......Page 87 2. Fourier-Maslov integral operators ......Page 121 3. Singularities of hyperbolic equations; examples and applications ......Page 146 1. Equations of principal type ......Page 158 2. Microlocal classification of pseudodifferential operators ......Page 184 3. Equations of subprincipal type ......Page 201 References ......Page 220 Index ......Page 224