Generalized Bernstein--Reznikov integrals

Mathematics – Classical Analysis and ODEs

Scientific paper

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Scientific paper

10.1007/s00208-010-0516-4

We find a closed formula for the triple integral on spheres in
$\mathbb{R}^{2n}\times\mathbb{R}^{2n}\times\mathbb{R}^{2n}$ 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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