Distance formulae and invariant subspaces, with an application to localization of zeros of the Riemann ζ-function
Annales de l'Institut Fourier, Tome 45 (1995) no. 1, p. 143-159
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 ζ de Riemann.
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 ζ-function.
@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {45},
     number = {1},
     year = {1995},
     pages = {143-159},
     doi = {10.5802/aif.1451},
     zbl = {0816.30026},
     mrnumber = {96c:47005},
     language = {en},
     url = {http://www.numdam.org/item/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, Tome 45 (1995) no. 1, pp. 143-159. doi : 10.5802/aif.1451. http://www.numdam.org/item/AIF_1995__45_1_143_0/

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