Complete interpolating sequences for Fock type spaces

TL;DR

This paper characterizes complete interpolating sequences in Fock-type spaces using geometric and separation criteria, extending previous results and providing explicit density conditions for sampling and interpolation.

Contribution

It offers a new geometric characterization of complete interpolating sequences in Fock-type spaces, generalizing prior work and including explicit density criteria.

Findings

Provides a geometric description of complete interpolating sequences.

Extends previous results on Riesz bases in Fock spaces.

Yields explicit density criteria for sampling and interpolation.

Abstract

We obtain a characterization of complete interpolating sequences in a class of Fock-type spaces with radial weights for which such sequences exist. Our criterion is formulated in terms of logarithmic separation and controlled perturbations of a reference sequence satisfying an Avdonin-type condition. This provides a geometric description of complete interpolating sequences and extends previous results of Borichev--Lyubarskii and Baranov--Belov--Borichev on Riesz bases of reproducing kernels in Fock-type spaces. It also yields explicit density criteria for sampling and interpolating sequences.