Two types of invariant Subspaces in the polydisc

Abstract

It is known that the structure of invariant subspaces of the Hardy space $H^2({\mathbb{D}}^n)$ on the polydisc ${\mathbb{D}}^n$ is very complicated; hence, we need good examples help us to understand the structure of invariant subspaces of $H^2({\mathbb{D}}^n)$. In this paper, we define two types of invariant subspaces of $H^2({\mathbb{D}}^n)$. Then, we give a characterization of these types invariant subspaces in view of the Beurling-Lax-Halmos Theorem. Unitary equivalence is also studied in this paper.

8 pages, this is a preliminary version of the paper and all comments/suggestions are welcome