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Article Dans Une Revue Journal of Functional Analysis Année : 2016

Bergman kernels, TYZ expansions and Hankel operators on the Kepler manifold

Résumé

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.
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Dates et versions

hal-01485442 , version 1 (08-03-2017)

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Hélène Bommier-Hato, Miroslav Engliš, El-Hassan Youssfi. Bergman kernels, TYZ expansions and Hankel operators on the Kepler manifold. Journal of Functional Analysis, 2016, 271 (2), pp.264 - 288. ⟨10.1016/j.jfa.2016.04.018⟩. ⟨hal-01485442⟩
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