A CHARACTERIZATION OF SUBMODULES VIA THE BEURLING-LAX-HALMOS THEOREM.

Shift invariant subspaces in the vector-valued Hardy space H²(E) play important roles in Nagy-Foias operator model theory. A theorem by Beurling, Lax and Halmos characterizes such invariant subspaces by operatorvalued inner functions ɵ(z). When E = H²(ⅅ), H²(E) is the Hardy space over the bidisk H²(ⅅ²). This paper shows that for some well-known examples of invariant subspaces in H²(ⅅ²), the function ɵ(z) turns out to be strikingly simple. [ABSTRACT FROM AUTHOR]