Mutually prime sequences of inner functions and the ranks of subspaces over the bidisk |
| |
Authors: | Email author" target="_blank">Kei?Ji?IzuchiEmail author Kou?Hei?Izuchi Yuko?Izuchi |
| |
Institution: | 1.Department of Mathematics,Niigata University,Niigata,Japan;2.Department of Mathematics, Faculty of Education,Yamaguchi University,Yamaguchi,Japan;3.Nishi-ku, Niigata,Japan |
| |
Abstract: | Let \({\{\varphi_n(z)\}_{n\ge0}}\) be a sequence of inner functions satisfying that \({\zeta_n(z):=\varphi_n(z)/\varphi_{n+1}(z)\in H^\infty(z)}\) for every n ≥ 0 and \({\{\varphi_n(z)\}_{n\ge0}}\) have no nonconstant common inner divisors. Associated with it, we have a Rudin type invariant subspace \({\mathcal{M}}\) of \({H^2(\mathbb{D}^2)}\) . We write \({\mathcal{N}= H^2(\mathbb{D}^2)\ominus\mathcal{M}}\) . If \({\{\zeta_n(z)\}_{n\ge0}}\) ia a mutually prime sequence, then we shall prove that \({rank_{\{T^\ast_z,T^\ast_w\}} \mathcal{N}=1}\) and \({rank_{\{\mathcal{F}^\ast_z\}}(\mathcal{M}\ominus w\mathcal{M})=1}\) , where \({\mathcal{F}_z}\) is the fringe operator on \({\mathcal{M}\ominus w\mathcal{M}}\) . |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|