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

Jean-François Burnol[1]

  • [1] Université Lille 1 UFR de Mathématiques Cité scientifique M2 F-59655 Villeneuve d’Ascq, France

Journal de Théorie des Nombres de Bordeaux (2004)

  • Volume: 16, Issue: 1, page 65-94
  • ISSN: 1246-7405

Abstract

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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.

How to cite

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Burnol, Jean-François. "Two complete and minimal systems associated with the zeros of the Riemann zeta function." Journal de Théorie des Nombres de Bordeaux 16.1 (2004): 65-94. <http://eudml.org/doc/249278>.

@article{Burnol2004,
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.},
affiliation = {Université Lille 1 UFR de Mathématiques Cité scientifique M2 F-59655 Villeneuve d’Ascq, France},
author = {Burnol, Jean-François},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {Riemann zeta function; Hilbert spaces; Fourier Transform},
language = {eng},
number = {1},
pages = {65-94},
publisher = {Université Bordeaux 1},
title = {Two complete and minimal systems associated with the zeros of the Riemann zeta function},
url = {http://eudml.org/doc/249278},
volume = {16},
year = {2004},
}

TY - JOUR
AU - Burnol, Jean-François
TI - Two complete and minimal systems associated with the zeros of the Riemann zeta function
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2004
PB - Université Bordeaux 1
VL - 16
IS - 1
SP - 65
EP - 94
AB - 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.
LA - eng
KW - Riemann zeta function; Hilbert spaces; Fourier Transform
UR - http://eudml.org/doc/249278
ER -

References

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