arXiv subjects

Hélène Bommier-Hato

Publications and source records attributed to Hélène Bommier-Hato.

2 recordsLinked to original sources

arXiv2018

De Branges spaces and Fock spaces

Relations between two classes of Hilbert spaces of entire functions, de Branges spaces and Fock-type spaces with non-radial weights, are studied. It is shown that any de Branges space can be realized as a Fock-type space with equivalent area norm, and several constructions of a representing weight are suggested. For some special classes of weights (e.g., weights depending on the imaginary part only) the corresponding de Branges spaces are explicitly described.

math.CV↗

arXiv2016

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 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.

math.CV↗