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Seminar on Complex Analysis (Gonchar Seminar)
March 20, 2017 17:00, Moscow, Steklov Mathematical Institute, Room 411 (8 Gubkina)
 


The Riemann Hypothesis and Beurling's theorem

V. V. Kapustin

St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences

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Abstract: Beurling's theorem about invariant subspaces in the Hardy spaces allows us to reformulate the Riemann Hypothesis about the zeros of the zeta function in the sense that a certain modification of the zeta function is an outer function. Unitary transplants of the construction into other Hilbert spaces give us equivalent reformulations of results for the Hardy class. Two such constructions will be considered. One of them is Beurling–Nyman's construction, and the other is connected with a formula established by Davenport.

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