On interpolating varieties for weighted spaces of entire functions

Abstract

Berenstein and Li recently gave a very complete description (in analytic and in geometric terms) of the interpolating varieties for various weighted spaces of entire and meromorphic functions in the complex plane. In this paper we use L2-estimates for\(\bar \partial \) (as in recent work of Berndtsson and Ortega Cerda) to give easier proofs of some related results. In particular, we recover the geometric characterization of interpolating varieties for the space of entire functions of order smaller or equal to ρ > 0. In the higher dimensional case, the same technique provides a sufficient condition for interpolation on discrete varieties. This condition is not necessary in general, and it complements the results of Ounaies and Li and Taylor on the subject.