Open Access$ \bar{\partial} $-equation look at analytic Hilbert's zero-locus theorem
Author(s) -
Xuebin Lv,
AUTHOR_ID,
J. Xiao,
Cheng Yuan,
AUTHOR_ID,
AUTHOR_ID
Publication year - 2021
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.009
Subject(s) - mathematics , blaschke product , fock space , pure mathematics , zero (linguistics) , mathematical physics , mathematical analysis , physics , quantum mechanics , philosophy , linguistics
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 $.