当前位置: X-MOL 学术J. Lond. Math. Soc. › 论文详情
The periodic dilation completeness problem: cyclic vectors in the Hardy space over the infinite‐dimensional polydisk
Journal of the London Mathematical Society ( IF 1.121 ) Pub Date : 2020-06-28 , DOI: 10.1112/jlms.12365
Hui Dan; Kunyu Guo

The classical completeness problem raised by Beurling and independently by Wintner asks for which ψ ∈ L 2 ( 0 , 1 ) , the dilation system { ψ ( k x ) : k = 1 , 2 , … } is complete in L 2 ( 0 , 1 ) , where ψ is identified with its extension to an odd 2‐periodic function on R . This difficult problem is nowadays commonly called as the periodic dilation completeness problem (PDCP). By Beurling's idea and an application of the Bohr transform, the PDCP is translated as an equivalent problem of characterizing cyclic vectors in the Hardy space H ∞ 2 over the infinite‐dimensional polydisk for coordinate multiplication operators. In this paper, we obtain lots of new results on cyclic vectors in the Hardy space H ∞ 2 . In almost all interesting cases, we obtain sufficient and necessary criterions for characterizing cyclic vectors, and hence in these cases we completely solve the PDCP. Our results cover almost all previous known results on this subject.
更新日期:2020-06-29

 

全部期刊列表>>
胸部和胸部成像专题
自然科研论文编辑服务
ACS ES&T Engineering
ACS ES&T Water
屿渡论文,编辑服务
鲁照永
华东师范大学
苏州大学
南京工业大学
南开大学
中科大
唐勇
跟Nature、Science文章学绘图
隐藏1h前已浏览文章
中洪博元
课题组网站
新版X-MOL期刊搜索和高级搜索功能介绍
ACS材料视界
x-mol收录
广东实验室
南京大学
王杰
南科大
刘尊峰
湖南大学
清华大学
王小野
中山大学化学工程与技术学院
试剂库存
天合科研
down
wechat
bug