A Finite Multiplicity Helson-Lowdenslager-De Branges Theorem

This paper proves two theorems. The first of these simplifies and lends clarity to the previous characterizations of the invariant subspaces of $S$, the operator of multiplication by the coordinate function $z$, on $L^2(\mathbb{T};\mathbb{C}^n)$, where $\mathbb{T}$ is the unit circle, by characterizing the invariant subspaces of $S^n$ on scalar valued $L^p$ ($0
Comment: 18 pages