Email this article 
A GENERALIZATION OF THE FIRST BEURLING AND MALLIAVIN THEOREM
- Authors: Vasilyev I.M.1
-
Affiliations:
- St. Petersburg Department of V.A. Steklov Institute of Mathematics of the Russian Academy of Sciences
- Issue: Vol 509, No 1 (2023)
- Pages: 83-86
- Section: MATHEMATICS
- URL: https://journals.rcsi.science/2686-9543/article/view/142175
- DOI: https://doi.org/10.31857/S2686954322600550
- EDN: https://elibrary.ru/CQEOWO
- ID: 142175
Cite item
Open Access
Access granted
Subscription Access
Abstract
In this paper, we announce a result that generalizes the first Beurling–Malliavin theorem. In other words, we give a new sufficient condition on a function, which guarantees that it belongs to the Beurling–Malliavin class of majorants. It is also shown that the main result of this article is sharp in many senses.
About the authors
I. M. Vasilyev
St. Petersburg Department of V.A. Steklov Institute of Mathematics of the Russian Academy of Sciences
Author for correspondence.
Email: milavas@mail.ru
Russian, Saint-Petersburg
References
- Belov Y., Havin V. The Beurling–Malliavin Multiplier Theorem and its analogs for the de Branges spaces. Springer series: Operator theory, ed. Alpay. 2015. V. 1. P. 581–609.
- Beurling A., Malliavin P. On Fourier transforms of measures with compact support, Acta Math. 1962. V. 107. P. 291–309.
- Bourgain J., Dyatlov S. Spectral gaps without the pressure condition, Annals of Math. 2018. V. 187. P. 825–867.
- De Branges L. Hilbert spaces of entire functions, Prentice-Hall, 1968.
- Havin V., Mashreghi J. Admissible majorants for model subspaces of H2, Part I: Slow winding of the generating inner function, Canad. J. Math. 2003. V. 55. Issue 6. P. 1231–1263.
- Havin V., Mashreghi J. Admissible majorants for model subspaces of H2, Part II : Fast winding of the generating inner function, Canad. J. Math. 2003. V. 55. Issue 6. P. 1264–1301.
- Kislyakov S., Perstneva P. Indicator functions with uniformly bounded Fourier sums and large gaps in the spectrum, Journal of Fourier Analysis and Applications. 2022.
- Makarov N., Poltoratski A. Beurling-Malliavin theory for Toeplitz kernels, Invent. Math. 2010. V. 180. № 3. P. 443–480.
- Mashregi D., Nazarov F., Khavin V. The Beurling–Malliavin multiplier theorem: The seventh proof, Algebra i Analiz. 2005. V. 17. № 5. P. 3–68.
- Nazarov F., Olevskii A. A Function with Support of Finite Measure and “Small” Spectrum, 50 Years with Hardy Spaces. In: Baranov A., Kisliakov S., Nikolski N. (eds) 50 Years with Hardy Spaces. Operator Theory: Advances and Applications, V. 261. Birkhäuser.
- Poltoratski A. Spectral gaps for sets and measures, Acta Math. 2012. V. 208. № 1. P. 151–209.
- Redheffer H. Completeness of sets of complex exponentials, Adv. Math. 1977. V. 24. Issue 1. P. 1–62.
- Vasilyev I. On the multidimensional Nazarov lemma, Proc. Amer. Math Soc. 2022. V. 150. № 4. P. 1601–1611.
- Vasilyev I. On the first Beurling–Malliavin Theorem, https://arxiv.org/pdf/2203.16674.pdf. 2022.
Supplementary files
