Distance formulae and invariant subspaces, with an application to localization of zeros of the Riemann ζ -function

Nikolai Nikolski

Annales de l'institut Fourier (1995)

  • Volume: 45, Issue: 1, page 143-159
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Nikolski, Nikolai. "Distance formulae and invariant subspaces, with an application to localization of zeros of the Riemann $\zeta $-function." Annales de l'institut Fourier 45.1 (1995): 143-159. <http://eudml.org/doc/75111>.

@article{Nikolski1995,
abstract = {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 $\zeta $-function.},
author = {Nikolski, Nikolai},
journal = {Annales de l'institut Fourier},
keywords = {invariant subspaces; distance formulae; reproducing kernels; Riemann -function},
language = {eng},
number = {1},
pages = {143-159},
publisher = {Association des Annales de l'Institut Fourier},
title = {Distance formulae and invariant subspaces, with an application to localization of zeros of the Riemann $\zeta $-function},
url = {http://eudml.org/doc/75111},
volume = {45},
year = {1995},
}

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
PB - Association des Annales de l'Institut Fourier
VL - 45
IS - 1
SP - 143
EP - 159
AB - 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 $\zeta $-function.
LA - eng
KW - invariant subspaces; distance formulae; reproducing kernels; Riemann -function
UR - http://eudml.org/doc/75111
ER -

References

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  9. [N] N.K. NIKOLSKI, Treatise on the shift operator, Springer-Verlag, Heidelberg, 1986. 
  10. [Ni] N.K. NIKOLSKI, Invitation aux techniques des espaces de Hardy, EDM, Université Bordeaux-1, 1992, p. 1-69. 
  11. [Nik] N.K. NIKOLSKI, Two problems on spectral synthesis, Lect. Notes Math., Springer-Verlag, 1043 (1984), 378-381. 
  12. [Ny] B. NYMAN, On some groups and semi-groups of translations, Thesis, Uppsala, 1950. 
  13. [Sh] N. SHIROKOV, Analytic functions smooth up to the boundary, Lect. Notes Math., v. 1312, Springer-Verlag, 1988. Zbl0656.30029MR90h:30087
  14. [V] V.I. VASYUNIN, On a biorthogonal function system related to the Riemann hypothesis, Algebra i Analiz (St. Petersburg Math. J.), to appear. Zbl0851.11051

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