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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)

Abstract

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.

Keywords

Pseudodifferential Operator Coadjoint Orbit Fourier Integral Operator Diffeomorphism Group Banach Manifold 
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 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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