Beurling Type Theorem on the Hilbert Space Generated by a Positive Sequence
Beurling Type Theorem on the Hilbert Space Generated by a Positive Sequence作者机构:School of Mathematical Sciences Dalian University of Technology Dalian 116024 P. R. China Department of Mathematics Physics and Information Engineering Jiaxing University Jiaxing 314001 P. R. China
出 版 物:《Acta Mathematica Sinica,English Series》 (数学学报(英文版))
年 卷 期:2019年第35卷第9期
页 面:1511-1519页
核心收录:
学科分类:07[理学] 0701[理学-数学] 070101[理学-基础数学]
基 金:Supported by NSFC(Grant Nos.11271332 and 11431011) the Fundamental Research Funds for the Central Universities NSFC(Grant No.11501249)
主 题:Beurling type theorem invariant subspace wandering subspace
摘 要:Let H^2(γ) be the Hilbert space over the bidisk D^2 generated by a positive sequence γ={γnm}n,m≥0. In this paper, we prove that the Beurling type theorem holds for the shift operator on H^2(γ) with γ={γnm}n,m≥0 satisfying certain series of inequalities. As a corollary, we give several applications to a class of classical analytic reproducing kernel Hilbert spaces over the bidisk D^2.