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On some Hilbert spaces of entire functions associated with the Fourier transform and Dirichlet and Riemann \(L\)-functions. (Sur certains espaces de Hilbert de fonctions entières, liés à la transformation de Fourier et aux fonctions \(L\) de Dirichlet et de Riemann.) (French. Abridged English version) Zbl 1057.11039
Summary: We consider a Sonine space of entire functions which is related to the Fourier transform, and which depends on a parameter \(\lambda\). We construct for \(\lambda >1\) a subspace which is associated with the zeta function of Riemann and we show that the quotient contains vectors intrinsically linked to the non-trivial zeros and to their possible multiplicities. A similar construction is possible for each Dirichlet \(L\)-function.

MSC:
11M06 \(\zeta (s)\) and \(L(s, \chi)\)
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
46E20 Hilbert spaces of continuous, differentiable or analytic functions
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