单位圆盘上再生■[z]-模的刚性

Rigidity of Reproducing ■[z]-Modules over the Unit Disk

主要研究单位开圆盘上■[z]-模的子模的刚性.证明了空间■_α(0<α<1)的子模具有刚性,这和Hardy空间的情况截然不同.本文还证明了Dirichlet空间的一类子模也具有刚性.

In this paper, we investigate the rigidity of submodules of L[z]-modules over the open unit disk. We prove that submodules of the space Hα（0 〈 α 〈 1） are rigid, which is completely different from the case in the usual Hardy space. Then we prove that in the Dirichlet space, the rigidity of submodules also exists under some mild assumption.