Resumen de Interpolating varieties for weighted spaces of entire functions in Cn

Bao Qin Li, Carlos A. Berenstein Cortés

• We prove in this paper that a given discrete variety $V$ in $\bold C^n$ is an interpolating variety for a weight $p$ if and only if $V$ is a subset of the variety $\{\xi \in \bold C^n: f_1(\xi)=f_2(\xi)= \cdots=f_n(\xi)=0\}$ of $m$ functions $f_1,\ldots,f_m$ in the weighted space the sum of whose directional derivatives in absolute value is not less than $\epsilon\exp(-Cp(\zeta)),\quad \zeta\in V$ for some constants $\epsilon$, $C>0$. The necessary and sufficient conditions will be also given in terms of the Jacobian matrix of $f_,\ldots,f_m.$ As a corollary, we solve an open problem posed by Berenstein and Taylor about interpolation for discrete varieties.