Contact geometry and linear differential equations
type: Item
instance of: scholarly article
title: Contact geometry and linear differential equations
zbMATH Open document ID: 0813.58003
author: Boris Sternin
author: Vladimir E. Nazaikinskii
author: Victor Shatalov
published in: De Gruyter Expositions in Mathematics
publication date: 1993-01-23T00:00:00Z
review text: This book divides into three chapters: I. Homogeneous functions, Fourier transformation, and contact structures, II. Fourier-Maslov operators, III. Applications to differential equations. The first chapter contains the presentation of the projective Fourier transformation. The authors show that the projective Fourier transformation may be defined by simple axioms and give explicit formulae for this transformation by integrals of residues of certain closed forms on projective spaces. In the next chapter they construct the theory of Fourier integral operators. The book ends with the applications of the theory to two classes of equations, namely, to equations of principal and subprincipal type which are defined within the theory of contact geometry.
Mathematics Subject Classification ID: 58-02
Mathematics Subject Classification ID: 58J40
Mathematics Subject Classification ID: 37J55
Mathematics Subject Classification ID: 53D10
Mathematics Subject Classification ID: 58C35
zbMATH DE Number: 53028
zbMATH Keywords: homogeneous phase space
zbMATH Keywords: Maslov operator
zbMATH Keywords: microlocal
zbMATH Keywords: symplectic structure
zbMATH Keywords: Fourier integral operators
zbMATH Keywords: contact geometry
reviewed by: Witold Mozgawa
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 53028