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Linus Lidman Bergqvist: Beurling type subspaces on the bidisc

Time: Wed 2023-02-22 11.00 - 12.00

Location: Albano, Cramérrummet

Participating: Linus Lidman Bergqvist (SU)

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A classical result due to Beurling says that every closed shift invariant subspace of the Hardy space is generated by an inner function. For the Hardy space on the bidisc, this is no longer true, and invariant subspaces can even be infinitely generated, However, in 1988 Mandrekar proved that an invariant subspace is generated by an inner function if and only if the the shift operators are doubly commuting on this subspace. In this talk we will go through some background to the problem of finding shift invariant subspaces, and present a new proof of Mandrekar's result which only relies on the theory of reproducing kernels.