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Contact geometry and linear differential equations. (English) Zbl 0813.58003
De Gruyter Expositions in Mathematics. 6. Berlin etc.: W. de Gruyter. ix, 216 p. (1992).
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.
Reviewer: W.Mozgawa (Lublin)

58-02 Research exposition (monographs, survey articles) pertaining to global analysis
58J40 Pseudodifferential and Fourier integral operators on manifolds
37J55 Contact systems
53D10 Contact manifolds, general
58C35 Integration on manifolds; measures on manifolds