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Analysis on Groups of Diffeomorphisms

  • Yuri E. Gliklikh
Part of the Theoretical and Mathematical Physics book series (TMP)

Abstract

By H s we denote the Sobolev space of functions such that the functions and their generalized derivatives up to order s belong to the functional space L 2. A detailed description of Sobolev spaces can be found, e.g., in (Egorov, 1984). An introduction to the manifold structure in functional sets can be found in (Eliasson, 1967). The reader may wish to consult (Ebin and Marsden, 1970) for details on the remaining material of this section.

Keywords

Tangent Space Tangent Bundle Exponential Mapping Manifold Structure Integral Lattice 
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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References

  1. 61.
    Ebin, D.G., Marsden, J.: Groups of diffeomorphisms and the motion of an incompressible fluid. Annals of Math. 92 (1), 102–163 (1970) CrossRefMathSciNetGoogle Scholar
  2. 62.
    Egorov, Yu.V.: Linear differential equations of principal type. Nauka, Moscow (1984) (Russian) MATHGoogle Scholar
  3. 64.
    Eliasson, H.I.: Geometry of manifolds of maps. J. Diff. Geometry. 1, 169-194 (1967) MATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Mathematics DepartmentVoronezh State UniversityVoronezhRussia

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