Interpolation by entire functions with growth conditions

Abstract

Let $A_p(\C)$ be the space of entire functions such that $|f(z)|\le A{e}^{Bp(z)}$ for some $A,B>0$ and let $V$ be a discrete sequence of complex numbers which is not a uniqueness set for $A_p(\C)$. We use $L^2$ estimates for the $\bar{\partial }$ equation to charaterize the trace of $A_p(\C)$ on $V$.