Two Types of Invariant Subspaces in the Polydisc

Abstract

It is known that the structure of invariant subspaces of the Hardy space H-2(D-n) on the polydisc D-n is very complicated; hence, we need good examples help us to understand the structure of invariant subspaces of H-2(D-n). In this paper, we define two types of invariant subspaces of H-2(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.