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A problem of continuity linked to the Riemann hypothesis. (Étude d’un problème de continuité lié à l’hypothèse de Riemann.) (French) Zbl 1138.11337

Summary: This work is devoted to a problem linked to the Beurling-Nyman’s criterion about the Riemann hypothesis. We study the continuity of the projection of the characteristic function of \((0,1)\) on a subspace of the square-integrable functions generated by dilated functions of the fractional part function. More generally, if \(y\) is a vector belonging to a Hilbert space \(H\), we study the function, which maps any closed and convex subspace \(C\) of \(H\) to the orthogonal projection of \(y\) on \(C\).

MSC:

11M26 Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses
46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)
46E15 Banach spaces of continuous, differentiable or analytic functions
47B38 Linear operators on function spaces (general)
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