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Fourier integral operators and Weyl-Hörmander calculus

  • Jean-Michel Bony

Abstract

It is well known that the space of classical pseudo-differential operators is invariant under conjugation by classical Fourier integral operators. However, the Weyl-Hörmander calculus [Hö1] [Hö2] provides a much larger framework for the theory of pseudo-differential operators. Any riemannian metric g on the phase space R n x × R n ξ, satisfying the conditions of definition 1.1, defines a graded algebra of pseudo-differential operators. The classical theory corresponds to a particular metric, namely g(dx,dξ) = dx 2 + dξ2/〈ξ〉2.

Keywords

Symplectic Form Pseudodifferential Operator Geodesic Distance Principal Symbol Fourier Integral Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Tokyo 1997

Authors and Affiliations

  • Jean-Michel Bony
    • 1
  1. 1.Centre de Mathématiques URA 169 CNRSEcole PolytechniquePalaiseau CedexFrance

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