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Research Article | Open Access

∂¯-equation look at analytic Hilbert's zero-locus theorem

Xiaofen Lv1, Jie Xiao2( ), Cheng Yuan3
Department of Mathematics, Huzhou University, Huzhou, Zhejiang 313000, China
Department of Mathematics and Statistics, Memorial University, St. John's, NL A1C 5S7, Canada
School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou, Guangdong 510520, China
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Abstract

Stemming from the Pythagorean Identity sin2⁡z+cos2⁡z=1 and Hörmander's L2-solution of the Cauchy-Riemann's equation ∂¯u=f on C, this article demonstrates a corona-type principle which exists as a somewhat unexpected extension of the analytic Hilbert's Nullstellensatz on C to the quadratic Fock-Sobolev spaces on C.

Keywords

∂¯u = fquadratic Fock-Sobolev spaceanalytic Hilbert's Nullstellensatz

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Electronic Research Archive
Volume 30 Issue 1,
January 2022
Pages 168-178
DOI: 10.3934/era.2022009

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Cite this article:
Lv X, Xiao J, Yuan C. ∂¯-equation look at analytic Hilbert's zero-locus theorem. Electronic Research Archive, 2022, 30(1): 168-178. https://doi.org/10.3934/era.2022009

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Received: 18 October 2021
Revised: 09 December 2021
Accepted: 09 December 2021
Published: 15 January 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)