It is proved that a subspace of a holomorphic Hilbert space is completely determined by their distances to the reproducing kernels. A simple rule is established to localize common zeros of a subspace of the Hardy space of the unit disc. As an illustration we show a series of discs of the complex plan free of zeros of the Riemann -function.
On démontre qu’un sous-espace d’un espace de Hilbert de fonctions holomorphes est complètement défini par ses distances aux noyaux reproduisants. Une méthode simple est proposée pour localiser les zéros simultanés d’un sous-espace de l’espace de Hardy. À titre d’illustration on montre une famille de disques du plan complexe sans zéro de la fonction de Riemann.
@article{AIF_1995__45_1_143_0,
author = {Nikolski, Nikolai},
title = {Distance formulae and invariant subspaces, with an application to localization of zeros of the {Riemann} $\zeta $-function},
journal = {Annales de l'Institut Fourier},
pages = {143--159},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {45},
number = {1},
year = {1995},
doi = {10.5802/aif.1451},
zbl = {0816.30026},
mrnumber = {96c:47005},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.1451/}
}
TY - JOUR AU - Nikolski, Nikolai TI - Distance formulae and invariant subspaces, with an application to localization of zeros of the Riemann $\zeta $-function JO - Annales de l'Institut Fourier PY - 1995 DA - 1995/// SP - 143 EP - 159 VL - 45 IS - 1 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.1451/ UR - https://zbmath.org/?q=an%3A0816.30026 UR - https://www.ams.org/mathscinet-getitem?mr=96c:47005 UR - https://doi.org/10.5802/aif.1451 DO - 10.5802/aif.1451 LA - en ID - AIF_1995__45_1_143_0 ER -
%0 Journal Article %A Nikolski, Nikolai %T Distance formulae and invariant subspaces, with an application to localization of zeros of the Riemann $\zeta $-function %J Annales de l'Institut Fourier %D 1995 %P 143-159 %V 45 %N 1 %I Association des Annales de l’institut Fourier %U https://doi.org/10.5802/aif.1451 %R 10.5802/aif.1451 %G en %F AIF_1995__45_1_143_0
Nikolski, Nikolai. Distance formulae and invariant subspaces, with an application to localization of zeros of the Riemann $\zeta $-function. Annales de l'Institut Fourier, Volume 45 (1995) no. 1, pp. 143-159. doi : 10.5802/aif.1451. http://www.numdam.org/articles/10.5802/aif.1451/
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