Sampling, interpolation and Riesz bases in small Fock spaces
Language
en
Article de revue
This item was published in
Journal de Mathématiques Pures et Appliquées. 2015, vol. 103, n° 6, p. 1358-1389
Elsevier
English Abstract
We give a complete description of Riesz bases of reproducing kernels in small Fock spaces. This characterization is in the spirit of the well known Kadets--Ingham 1/4 theorem for Paley--Wiener spaces. Contrarily to the ...Read more >
We give a complete description of Riesz bases of reproducing kernels in small Fock spaces. This characterization is in the spirit of the well known Kadets--Ingham 1/4 theorem for Paley--Wiener spaces. Contrarily to the situation in Paley--Wiener spaces, a link can be established between Riesz bases in the Hilbert case and corresponding complete interpolating sequences in small Fock spaces with associated uniform norm. These results allow to show that if a sequence has a density stricly different from the critical one then either it can be completed or reduced to a complete interpolating sequence. In particular, this allows to give necessary and sufficient conditions for interpolation or sampling in terms of densities.Read less <
English Keywords
Riesz bases
small Fock spaces
Sampling
interpolation
de Branges spaces
Bari's theorem
Origin
Hal imported