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

Hélène Bommier-Hato; Miroslav Engliš; El-Hassan Youssfi

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

Complex Variables 2016-01-15 v1

Authors: Hélène Bommier-Hato , Miroslav Engliš , El-Hassan Youssfi

Abstract

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.

Keywords

Bergman kernels Kepler manifold TYZ expansions Hankel operators reproducing kernels balanced metrics invariant measures

Cite

@article{arxiv.1601.03721,
  title  = {Bergman kernels, TYZ expansions and Hankel operators on the Kepler manifold},
  author = {Hélène Bommier-Hato and Miroslav Engliš and El-Hassan Youssfi},
  journal= {arXiv preprint arXiv:1601.03721},
  year   = {2016}
}

Comments

20 pages; submitted to J. Funct. Anal. on January 16, 2015

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

Abstract

Keywords

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