Have a personal or library account? Click to login
On the Connection Between the Beurling-Malliavin Density and the Asymptotic Density Cover

On the Connection Between the Beurling-Malliavin Density and the Asymptotic Density

By: Rita Giuliano and  Georges Grekos  
Open Access
|Feb 2025

References

  1. BARANOV, A.—BELOV, Y.—ULANOVSKII, A.: Gap problem for separated sequences without pain J. Fourier Anal. Appl. 23 (2017), 877–885.
  2. BEURLING, A.—MALLIAVIN, P.: On the closure of characters and the zeros of entire functions,Acta Math. 118 (1967), 79–93.
  3. PALEY, RAYMOND E. A. C.—WIENER, N.: Fourier transforms in the complex domain, (Reprint of the 1934 original.) American Mathematical Society Colloquium Publications, Vol. 19. American Mathematical Society, Providence, RI, 1987.
  4. BINGHAM, N. H.—GOLDIE, C. M.—TEUGELS, J. L.: Regular Variation. Encyclopedia of Mathematics and its Applications, Vol. 27. Cambridge University Press, Cambridge, 1989.
  5. FUCHS, A.—GIULIANO ANTONINI, R.: Théorie générale des densités, [The general theory of densities] Rend. Accad. Naz. Sci. XL Mem. Mat. (5) 14 (1990), no. 1, 253–294.
  6. GIULIANO, R.—GREKOS, G.—MIŠÍK, L.: The Beurling–Malliavin density, the Pólya density and their connection, Unif. Distrib. Theory 19 (2024), no 1, 67–86.
  7. KHABIBULLIN, B. N.: Nonconstructive proofs of the Beurling-Malliavin theorem on the radius of completeness, and nonuniqueness theorems for entire functions,Izv.Math. 45, (1995), 125–149.
  8. KAHANE, J.-P.: Travaux de Beurling et Malliavin,Séminaire Bourbaki 14, Talk, no. 225 (1962/1962), 27–39, https://eudml.org/doc/109633.
  9. KOOSIS, P.: The Logarithmic Integral II. In: Cambridge Studies in Advanced Mathematics. Vol 21. Cambridge University Press. Cambridge, 1992.
  10. KRASICHKOV-TERNOVSKIȈI, I. F.: An interpretation of the Beurling–Malliavin theory on the radius of completeness, Math. USSR-Sbornik 66 (1990), no. 2, 405–429.
  11. OLIVIER, L.: Remarques sur les séries infinies et leur convergence, J. Reine Angew. Math. 2 (1827), 31–44.
  12. POLTORATSKI, A.: Spectral gaps for sets and measures,Acta Math. 208 (2012), no. 1, 151–209.
  13. POLTORATSKI, A.: Completeness of exponentials. In: Beurling-Malliavin and Type Problems (2018), https://eta.impa.br/icm_files/invited/section-8/IL.8.18.pdf, accessible on 2023/12/05.
  14. POLTORATSKI, A.: Toeplitz methods in completeness and spectral problems.In: Proceedings of the International Congress of Mathematicians—Rio de Janeiro 2018. Vol. III. Invited lectures, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2018. pp. 1771–1796.
  15. REDHEFFER, R.: Two consequences of the Beurling–Malliavin theory,Proc. Am. Math. Soc. 36 (1972), no. 1, 116–122.
  16. ŠALÁT, T.: On subseries,Math. Z. 85 (1964), 209–225.
DOI: https://doi.org/10.2478/udt-2024-0006 | Journal eISSN: 2309-5377 | Journal ISSN: 1336-913X
Language: English
Page range: 67 - 86
Submitted on: Mar 30, 2024
Accepted on: Sep 23, 2024
Published on: Feb 24, 2025
Published by: Slovak Academy of Sciences, Mathematical Institute
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2025 Rita Giuliano, Georges Grekos, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.