Education
06.2016 — D.Sc. in Mathematics and Physics («Real, Complex and Functional Analysis»)
Thesis title: Hilbert Spaces of Entire Functions (Systems of Reproducing kernels, Bases, Completeness of Mixed Systems, Spectral Synthesis Problems)
05.2008 — Ph.D. (C.Sc.) in Mathematics and Physics («Real, Complex and Functional Analysis»)
Thesis title: Moduli of Functions in Model Subspaces of Hardy Space H^2
Advisor: V.P. Khavin
06.2003 — Specialist Degree in Mathematics (summa cum laude)
Institution: St. Petersburg State University
Scientific interests
My research interests lie in several areas of complex and harmonic analysis, time-frequency analysis and spectral theory.
1. Time-frequency analysis. We study properties of systems of time-frequency shifts of a given window function g in L^2(R). Such systems are called Gabor systems. The main results are related to the frame property which guarantees reasonable time-frequency representation. We are mostly interested in windows with good analytic properties (Gaussians, Cauchy kernels, rational functions, e.t.c.). In addition we study the completeness and minimality of such systems. One more theme is a sampling in shift-invariant subspaces V_g of L^2(R). References: [P1,2,6,7,10,12,20,28].
2. Spectral synthesis. We consider the spectral synthesis property for systems of exponentials and other systems of reproducing kernels of Hilbert spaces of entire functions (Paley-Wiener spaces, Fock type spaces e.t.c.). Such problems are closely connected to the so-called mixed completeness problems, i.e. completeness problems for the union of two systems of different nature, for a example a system from exponentials and its biorthogonal system. Another topic concerns a synthesis problem for differentiation operator in C^\infty(R). This problem was posed by B. Korenblum. In particular, our technique lead us to the negative solution to the Newman-Shapiro conjecture which was stated in 1966. References: [3,5,8,15,17,19,20,23,26,30,32,34,35].
3. Geometrical properties for systems of reproducing kernels. We study completeness, interpolation and Riesz basis properties for systems of reproducing kernels in the de Branges, Fock-type spaces and some other analytic function spaces. References: [P2,1,9,11,18,22,25,27,33,36,37,38,39].
4. Spectral theory. We study the connection between canonical systems on the interval (or half-axis) and properties of the corresponding de Branges spaces. The main results describe the correspondence between properties of the Hamiltonians and spectral measures. References: [4,14,16,24,31].
5. Other works: References: [13,21,29,40,41,42,43].
Selected publications
- Y. Belov, A. Kulikov, Y. Lyubarskii, Gabor frames for rational functions, Inventiones Mathematicae, 231, 431–466 (2023).
- Y. Belov, A. Borichev, The Newman-Shapiro problem, Journal of the European Mathematical Society (JEMS), 25 (2023), no. 4, pp. 1227–1251.
- A. Baranov, Y. Belov, Synthesizable differentiation-invariant subspaces, (2019), Geometric and Functional Analysis, 29(1), pp. 44-71.
- Y. Belov, Y. Lyubarskii, On summation of non-harmonic Fourier series, Constructive Approximation, (2016), Vol. 43:2, рр. 291–309.
- A. Baranov, Y. Belov, A. Borichev, Spectral synthesis in de Branges spaces, Geometric and Functional Analysis, (2015), Vol. 25, Iss. 2: pp. 417–452.
- Y. Belov, Uniqueness of Gabor series, Applied and Computational Harmonic Analysis 39 (2015), pp. 545–551.
- A. Baranov, Y.Belov, A.Borichev, Hereditary completeness for systems of exponentials and reproducing kernels, Advances in Mathematics 235 (2013), 525–554.
- Y. Belov, T. Mengestie, K. Seip, Discrete Hilbert transforms on sparse sequences, Proc. of London Math. Society (2011), Vol. 103, 73–105.
Additional Information
j_b_juri_belov@mail.ru
My curriculum vitae.
A complete list of my publications and preprints.
Teaching
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