We study the Hilbert space obtained by completing the space of all smooth and compactly supported functions on the real line with respect to the hermitian form arising from the Weil distribution under the Riemann hypothesis. It turns out that this Hilbert space is isomorphic to a de Branges space by a composition of the Fourier transform and a simple map. This result is also applied to state a new equivalence condition for the Riemann hypothesis.
Control theory and the Riemann hypothesis: A roadmap
Pair correlation of the zeros of the derivative of the Riemann $ξ$-function
Riemann Hypothesis: a special case of the Riesz and Hardy-Littlewood wave and a numerical treatment of the Baez-Duarte coefficients up to some billions in the k-variable
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