Beurling's theorem for the Hardy operator on $L^2[0,1]$

preprint2022arXivOpen access

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.

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Beurling's theorem for the Hardy operator on $L^2[0,1]$

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Beurling's theorem for the Hardy operator on L2[0,1]L^2[0,1]L2[0,1]

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Beurling's theorem for the Hardy operator on $L^2[0,1]$