Complete Interpolating sequences for small Fock Spaces

Abstract

We give a characterization of complete interpolating sequences for the Fock spaces ${\mathcal{F}}_{\phi }^p,1\le p<\infty$, where $\phi (z)=\alpha {\left({\log }^{+}|z|\right)}^2,\alpha >0$. Our results are {analogous} to the classical Kadets-Ingham's $1/4-$Theorem on perturbation of Riesz bases of complex exponentials, and they answer a question asked by A. Baranov, A. Dumont, A. Hartmann and K. Kellay in \cite[page 31]{baranov2015sampling}.

References in corpus (2)

• Discrete Hilbert transforms on sparse sequences
• Riesz bases of reproducing kernels in small Fock spaces