Burnol: Two complete and minimal systems associated with the zeros of the Riemann zeta function

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Jean-François Burnol
Two complete and minimal systems associated with the zeros of the Riemann zeta function
Journal de théorie des nombres de Bordeaux, 16 no. 1 (2004), p. 65-94, doi: 10.5802/jtnb.434
Article PDF | Reviews MR 2145573 | Zbl 02184632 | 1 citation in Cedram
Keywords: Riemann zeta function; Hilbert spaces; Fourier Transform

Résumé - Abstract

We link together three themes which had remained separated so far: the Hilbert space properties of the Riemann zeros, the “dual Poisson formula” of Duffin-Weinberger (also named by us co-Poisson formula), and the “Sonine spaces” of entire functions defined and studied by de Branges. We determine in which (extended) Sonine spaces the zeros define a complete, or minimal, system. We obtain some general results dealing with the distribution of the zeros of the de-Branges-Sonine entire functions. We draw attention onto some distributions associated with the Fourier transform and which we introduced in our earlier works.

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