文献类型：期刊文献

英文题名：SUBMODULES OF THE HARDY MODULE IN INFINITELY MANY VARIABLES

作者：Dan, Hui[1];Guo, Kunyu[1];Huang, Hansong[2]

机构：[1]Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China;[2]East China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

年份：2018

卷号：80

期号：2

起止页码：375

外文期刊名：JOURNAL OF OPERATOR THEORY

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000448389300004)】；

基金：The authors would like to express their heartfelt thankfulness to the referee for providing numerous valuable suggestions to make this paper more readable. This work is partially supported by National Natural Science Foundation of China.

语种：英文

外文关键词：The Hardy module; infinitely many variables; closed ideals; Ahern-Clark's theorem

摘要：This paper is concerned with polynomially generated submodules of the Hardy module H-2 (D-2(infinity)). Since the polynomial ring P-infinity in infinitely many variables is not Noetherian, some standard tricks for finitely many variables fail to work. Therefore, we need to introduce new techniques to the situation of infinitely many variables. It is shown that some classical results of H-2 (D-n) remain valid for infinitely many variables. However, some new phenomena indicate that the Hardy module H-2 (D-2(infinity)) diverges considerably from the case in finitely many variables.