Beurling's theorem for the Hardy operator on L2[0,1]

We prove that the invariant subspaces of the Hardy operator on L-2[0, 1] are the spaces that are limits of sequences of finite dimensional spaces spanned by monomial functions.

Automated summary

We prove that the invariant subspaces of the Hardy operator on L-2[0, 1] are the limit spaces of sequences of finite dimensional spaces spanned by monomial functions.