Beurling–Lax theorem

In mathematics, the  Beurling–Lax theorem is a theorem due to and  which characterizes the shift-invariant subspaces of the Hardy space $$H^2(\mathbb{D},\mathbb{C})$$. It states that each such space is of the form


 * $$ \theta H^2(\mathbb{D},\mathbb{C}), $$

for some inner function $$\theta$$.