Generalized Bernstein--Reznikov integrals
Jean-Louis Clerc, Toshiyuki Kobayashi, Bent {\O}rsted, Michael Pevzner

TL;DR
This paper derives a closed-form expression for a class of triple integrals involving symplectic forms on spheres, providing new proofs and extending results to linear and conformal structures.
Contribution
It introduces a novel closed-form formula for symplectic kernel integrals on spheres, generalizing the Bernstein--Reznikov integral and applying to broader geometric structures.
Findings
Derived a closed-form formula for symplectic form-based integrals
Provided a new proof of the Bernstein--Reznikov integral in the case n=1
Extended the method to linear and conformal structures
Abstract
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 case. Our method also applies for linear and conformal structures.
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