Publications

Preprints

• Ole  Fredrik Brevig, Aleksei Kulikov, Kristian Seip, Ilya Zlotnikov, 

Contractive Hardy--Littlewood inequalities in the Dirichlet range,

preprint: https://arxiv.org/abs/2510.14333

Published papers

• Alexander Ulanovskii, Ilya Zlotnikov,  

Stability of shifts, interpolation, and spectrum of atomic measures, Journal of the London Mathematical Society,  112(3), e70267, (2025)

DOI: https://doi.org/10.1112/jlms.70267 (see also preprint: https://arxiv.org/abs/2410.08682  entitled Stability of shifts, interpolation, and crystalline measures, which contains additional results not included in the published version).

• Alexander Ulanovskii, Ilya Zlotnikov,
  Sampling  in quasi shift-invariant spaces and  Gabor frames generated by ratios of exponential polynomials,  Mathematische Annalen,  391, 3429–3456, (2025)
  DOI:   https://doi.org/10.1007/s00208-024-03011-7,  preprint: https://arxiv.org/abs/2402.03090

• Markus Faulhuber, Irina Shafkulovska, Ilia Zlotnikov,

On the Frame Property of Hermite Functions and Exploration of their Frame Sets,  Journal of Fourier Analysis and Applications, 31, 21 (2025),  (Special Issue on the Occasion of Karlheinz Gröchenig's 65th Birthday)

DOI: https://doi.org/10.1007/s00041-025-10153-y ,  preprint: https://arxiv.org/abs/2403.10503

• Markus Faulhuber, Irina Shafkulovska, Ilia Zlotnikov,
  A note on energy minimization in dimension 2,  Proceedings of the American Mathematical Society Ser. B 11 (2024), 664-679

DOI: https://doi.org/10.1090/bproc/247, preprint: https://arxiv.org/abs/2306.16266

• José  Luis Romero, Alexander Ulanovskii, Ilya Zlotnikov,
  Sampling in the shift-invariant space generated by the bivariate Gaussian function, Journal of Functional Analysis, Volume 287, Issue 9, 110600,  (2024)
  DOI:  https://doi.org/10.1016/j.jfa.2024.110600, preprint: https://arxiv.org/abs/2306.13619

• Aleksei Kulikov, Alexander Ulanovskii, Ilya Zlotnikov,
  Completeness of Certain Exponential Systems and Zeros of Lacunary Polynomials, Advances in Mathematics, Volume 421, 109016, (2023)
  DOI:  https://doi.org/10.1016/j.aim.2023.109016,   preprint: https://arxiv.org/abs/2210.00504
  
  

• Alexander Ulanovskii, Ilya Zlotnikov,
  On geometry of the unit ball of Paley-Wiener space over two symmetric intervals, International Mathematics Research Notices, Volume 2023, Issue 8, 6329–6363, (2023)
  DOI:  https://doi.org/10.1093/imrn/rnac043,  preprint: https://arxiv.org/abs/2108.08093
  
  

• Aleksei Kulikov, Ilya Zlotnikov,
  Contractive projections in Paley-Wiener spaces,  Proceedings of the American Mathematical Society, Volume 151, Number 4, Pages 1637–1641, (2023),
  DOI:  https://doi.org/10.1090/proc/16336,   preprint: https://arxiv.org/abs/2207.09278
  
  

• Alexander Rashkovskii, Alexander Ulanovskii, Ilya Zlotnikov,
  On 2-dimensional mobile sampling,  Applied and Computational Harmonic Analysis, Volume 62, 1-23, (2023),
  DOI: https://doi.org/10.1016/j.acha.2022.08.001,  preprint: https://arxiv.org/abs/2005.11193
  
  

• Ilya Zlotnikov,
  On planar sampling with Gaussian kernel in spaces of bandlimited functions, Journal of Fourier Analysis and Applications, Volume 28, Issue 3, (2022),
  DOI: https://doi.org/10.1007/s00041-022-09948-0,  preprint: http://arxiv.org/abs/2104.09573
  
  

• Dmitriy Stolyarov, Vasily Vasyunin, Pavel Zatitskiy, Ilya Zlotnikov,
  Sharp moment estimates for martingales with uniformly bounded square functions, Mathematische Zeitschrift, Volume 302, Issue 1, 181-217, (2022),
  DOI: https://doi.org/10.1007/s00209-022-03064-x,   preprint: https://arxiv.org/abs/2102.11568
  
  

• Vasily Vasyunin, Pavel Zatitskiy, Ilya Zlotnikov,
  Sharp multiplicative inequalities with BMO II, Journal of Mathematical Analysis and Applications, Volume 515, Issue 2, 126430, (2022),
  DOI: https://doi.org/10.1016/j.jmaa.2022.126430,   preprint: https://arxiv.org/abs/2111.05565
  
  

• Alexander Ulanovskii, Ilya Zlotnikov,
  Reconstruction  of bandlimited functions from space-time samples, Journal of Functional Analysis, Volume 280, Issue 9, 108962, (2021),
  DOI: https://doi.org/10.1016/j.jfa.2021.108962,  preprint: https://arxiv.org/abs/2007.11366
  
  

• Kislyakov S.V., Zlotnikov I.K.,
  Interpolation for intersections of Hardy-type spaces, Israel Journal of Mathematics, Volume  239, Issue 1, 21-38,(2020),
  DOI: https://doi.org/10.1007/s11856-020-2029-5,   preprint: https://arxiv.org/abs/1903.09959
  
  

• Kislyakov S.V., Zlotnikov I.K.,
  Grothendieck theorem for some uniform algebras and modules over them, Journal of Mathematical Sciences, Volume 251, Issue 2, 230-238 (2020),
  DOI: https://doi.org/10.1007/s10958-020-05084-6
  
  

• Dmitriy Stolyarov, Vasily Vasyunin, Pavel Zatitskiy, Ilya Zlotnikov,
  Distribution of martingales with bounded square functions, Comptes Rendus Mathematique, Volume 357, Issue 8, 671-675, (2019),
  DOI: https://doi.org/10.1016/j.crma.2019.08.003
  
  

• Kislyakov S.V., Zlotnikov I.K.,
  Coinvariant subspaces of the shift operator and interpolation, Analysis Mathematica, Volume 44, Issue 2, 219-236, (2018),
  DOI: https://doi.org/10.1007/s10476-018-0207-z
  
  

•  Zlotnikov, I.K.,
  Problem of ideals in the algebra $ H^{\infty}$ for some spaces of sequences, Saint-Petersburg Mathematical Journal, Volume 29, Issue 5, 749-759, (2018),
  DOI:  https://doi.org/10.1090/spmj/1514
  
  

•  Zlotnikov, I.K.,
  Estimates in the problem of ideals in the algebra $H^{\infty}$,  Journal of Mathematical Sciences, Volume 229, Issue 5, 528-533, (2018),
  DOI: https://doi.org/10.1007/s10958-018-3695-2