Développement TYZ et opérateurs de Hankel sur la variété de Kepler

For a class of O(n + 1, R) invariant measures on the Kepler manifold possessing finite moments of all orders, we describe the
reproducing kernels of the associated Bergman spaces, discuss the corresponding asymptotic expansions of Tian-Yau-Zelditch, and study the relevant Hankel operators with conjugate holomorphic symbols. Related reproducing kernels on the minimal ball are also discussed. Finally, we observe that the Kepler manifold either does not admit balanced metrics, or such metrics are not unique.