Inspired by Olevskii and Ulanovskii [12], we introduce the concept of d-approximate interpolation in weighted Bargmann-Fock spaces as a natural extension of the classical concept of interpolation. We then show that d-approximate interpolation sets satisfy a density condition, similar to the one that classical interpolation sets satisfy. More precisely, we show that the upper Beurling density of any $d$-approximate interpolation set must be bounded from above by 1/(1-d²).

Research of the second author was supported in part by National Science Foundation DMS grant number 1600874.