Geometric conditions for interpolation in weighted spaces of entire functions

Abstract

We use $L^2$ estimates for the $\bar{\partial }$ equation to find geometric conditions on discrete interpolating varieties for weighted spaces $A_p(\C)$ of entire functions such that $|f(z)|\le A{e}^{Bp(z)}$ for some $A,B>0$. In particular, we give a characterization when $p(z)=e^{|z|}$ and more generally when $\ln p(e^r)$ is convex and $\ln p(r)$ is concave.