Riesz bases of reproducing kernels in Fock type spaces

TL;DR

This paper investigates conditions under which Fock spaces with radial weights have Riesz bases of normalized reproducing kernels, establishing a growth criterion for the weight function.

Contribution

It characterizes the existence of Riesz bases in Fock spaces based on the growth rate of the radial weight function, specifically when it grows no faster than a squared logarithm.

Findings

Riesz bases exist if and only if the weight growth is at most quadratic in log x.

The paper provides a precise growth condition linking weight behavior to basis properties.

It advances understanding of basis structures in weighted Fock spaces.

Abstract

In a scale of Fock spaces $\mathcal F_\varphi$ with radial weights $\varphi$ we study the existence of Riesz bases of (normalized) reproducing kernels. We prove that these spaces possess such bases if and only if $\varphi(x)$ grows at most like $(\log x)^2$.