A short proof of Cartan's Nullstellensatz for entire functions in ${\mathbb{C}}^n$

Abstract

Using the fact that the maximal ideals in the polydisk algebra are given by the kernels of point evaluations, we derive a simple formula that gives a solution to the Bézout equation in the space of all entire functions of several complex variables. Thus a short and easy analytic proof of Cartan's Nullstellensatz is obtained.

arXiv comment4 pages

References in corpus (1)

• Simultaneous Stabilization in $A_{\mathbb{R}}(\mathbb{D})$