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Journal of Mathematical Sciences

, Volume 141, Issue 4, pp 1432–1451 | Cite as

Canonical representations on two-sheeted hyperboloids

  • V. F. Molchanov
Article
  • 31 Downloads

Abstract

The two-sheeted hyperboloid \(\mathcal{L}\) in ℝn can be identified with the unit sphere Ω in ℝn with the equator removed. Canonical representations of the group G = SO 0(n − 1, 1) on \(\mathcal{L}\) are defined as the restrictions to G of the representations of the overgroup \(\tilde G\) = SO 0(n, 1) associated with a cone. They act on functions and distributions on the sphere Ω. We decompose these canonical representations into irreducible constituents and decompose the Berezin form. Bibliography: 12 titles.

Keywords

Symmetric Space Spherical Function Fourier Component Inversion Formula Boundary Representation 
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, Inc. 2007

Authors and Affiliations

  • V. F. Molchanov
    • 1
  1. 1.G. R. Derzhavin Tambov State UnversityTambovRussia

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