Generalized Bernstein–Reznikov integrals

We find a closed formula for the triple integral on spheres in whose kernel is given by powers of the standard symplectic form. This gives a new proof to the Bernstein–Reznikov integral formula in the n  = 1 case. Our method also applies for linear and conformal structures.

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Bibliographic Details
Published in:Mathematische annalen 2011-02, Vol.349 (2), p.395-431
Main Authors: Clerc, Jean-Louis, Kobayashi, Toshiyuki, Ørsted, Bent, Pevzner, Michael
Format: Article
Language:English
Subjects:
Classical Analysis and ODEs
Mathematics
Mathematics and Statistics
Representation Theory
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Description
Summary:We find a closed formula for the triple integral on spheres in whose kernel is given by powers of the standard symplectic form. This gives a new proof to the Bernstein–Reznikov integral formula in the n  = 1 case. Our method also applies for linear and conformal structures.
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-010-0516-4