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

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 conjugat...

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Bibliographic Details
Published in:Journal of functional analysis 2016-07, Vol.271 (2), p.264-288
Main Authors: Bommier-Hato, Hélène, Engliš, Miroslav, Youssfi, El-Hassan
Format: Article
Language:English
Subjects:
Balanced metric
Bergman kernel
Kepler manifold
Mathematics
Tian–Yau–Zelditch expansion
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Summary: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.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2016.04.018