$ \bar{\partial} $-equation look at analytic Hilbert's zero-locus theorem

Abstract

<abstract><p>Stemming from the Pythagorean Identity $ \sin^2z+\cos^2z = 1 $ and Hörmander's $ L^2 $-solution of the Cauchy-Riemann's equation $ \bar{\partial}u = f $ on $ \mathbb C $, this article demonstrates a corona-type principle which exists as a somewhat unexpected extension of the analytic Hilbert's Nullstellensatz on $ \mathbb C $ to the quadratic Fock-Sobolev spaces on $ \mathbb C $.</p></abstract>