Fock type spaces with Riesz bases of reproducing kernels and de Branges spaces

Anton Baranov (1, 2) , Yurii Belov (3) , Alexander Borichev (4, 1)

1 SPbU - St Petersburg State University
2 HSE - Vysšaja škola èkonomiki = National Research University Higher School of Economics [Moscow]
3 Chebyshev Laboratory
4 I2M - Institut de Mathématiques de Marseille

We describe the radial Fock type spaces which possess Riesz bases of normalized reproducing kernels and which are (are not) isomorphic to de Branges spaces in terms of the weight functions.

Mots clés: Fock spaces; de Branges spaces; Riesz bases; reproducing kernels

Domaines: Variables complexes [math.CV]; Analyse fonctionnelle [math.FA]

Anton Baranov, Yurii Belov, Alexander Borichev. Fock type spaces with Riesz bases of reproducing kernels and de Branges spaces. Studia Mathematica, 2017, 236 (2), pp.127 - 142. ⟨10.4064/sm8504-9-2016⟩. ⟨hal-01550572⟩