∂¯-equation look at analytic Hilbert's zero-locus theorem
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 Hilbe...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2022-01-01
|
| Series: | Electronic Research Archive |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2022009?viewType=HTML |
| _version_ | 1811182658314567680 |
|---|---|
| author | Xiaofen Lv Jie Xiao Cheng Yuan |
| author_facet | Xiaofen Lv Jie Xiao Cheng Yuan |
| author_sort | Xiaofen Lv |
| collection | DOAJ |
| description | 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 $. |
| first_indexed | 2024-04-11T09:35:33Z |
| format | Article |
| id | doaj.art-573becb9f75c41c6a1aec613d9232386 |
| institution | Directory Open Access Journal |
| issn | 2688-1594 |
| language | English |
| last_indexed | 2024-04-11T09:35:33Z |
| publishDate | 2022-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj.art-573becb9f75c41c6a1aec613d92323862022-12-22T04:31:44ZengAIMS PressElectronic Research Archive2688-15942022-01-0130116817810.3934/era.2022009∂¯-equation look at analytic Hilbert's zero-locus theoremXiaofen Lv 0Jie Xiao1 Cheng Yuan21. Department of Mathematics, Huzhou University, Huzhou, Zhejiang 313000, China2. Department of Mathematics and Statistics, Memorial University, St. John's, NL A1C 5S7, Canada3. School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou, Guangdong 510520, ChinaStemming 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 $. https://www.aimspress.com/article/doi/10.3934/era.2022009?viewType=HTMLquadratic fock-sobolev spaceanalytic hilbert's nullstellensatz$ \bar{\partial}u=f $ |
| spellingShingle | Xiaofen Lv Jie Xiao Cheng Yuan ∂¯-equation look at analytic Hilbert's zero-locus theorem Electronic Research Archive quadratic fock-sobolev space analytic hilbert's nullstellensatz $ \bar{\partial}u=f $ |
| title | ∂¯-equation look at analytic Hilbert's zero-locus theorem |
| title_full | ∂¯-equation look at analytic Hilbert's zero-locus theorem |
| title_fullStr | ∂¯-equation look at analytic Hilbert's zero-locus theorem |
| title_full_unstemmed | ∂¯-equation look at analytic Hilbert's zero-locus theorem |
| title_short | ∂¯-equation look at analytic Hilbert's zero-locus theorem |
| title_sort | ∂¯ equation look at analytic hilbert s zero locus theorem |
| topic | quadratic fock-sobolev space analytic hilbert's nullstellensatz $ \bar{\partial}u=f $ |
| url | https://www.aimspress.com/article/doi/10.3934/era.2022009?viewType=HTML |
| work_keys_str_mv | AT xiaofenlv equationlookatanalytichilbertszerolocustheorem AT jiexiao equationlookatanalytichilbertszerolocustheorem AT chengyuan equationlookatanalytichilbertszerolocustheorem |