The Lie Group Structure of Diffeomorphism Groups and Invertible Fourier Integral Operators with Applications

  • Malcolm Adams
  • Tudor Ratiu
  • Rudolf Schmid
Part of the Mathematical Sciences Research Institute Publications book series (MSRI, volume 4)


This is a survey of basic facts about the differentiable structure of infinite dimensional Lie groups. The groups of diffeomorphisms and of invertible Fourier integral operators on a compact manifold have a structure which is weaker than that of a Lie group in the classical sense. This differentiable structure is called ILH (inverse limit of Hilbert) Lie group. We indicate applications to the well-posedness problem, to hydrodynamics, plasma physics, general relativity, quantum field theory, and completely integrable PDE’s.


Pseudodifferential Operator Coadjoint Orbit Fourier Integral Operator Diffeomorphism Group Banach Manifold 
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Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • Malcolm Adams
    • 1
  • Tudor Ratiu
    • 2
    • 3
  • Rudolf Schmid
    • 3
    • 4
  1. 1.Institute for Advanced StudyPrincetonUSA
  2. 2.Department of MathematicsUniversity of ArizonaTucsonUSA
  3. 3.Mathematical Sciences Research InstituteBerkeleyUSA
  4. 4.Department of MathematicsYale UniversityNew HavenUSA

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