Ilia Zlotnikov

activity

20202026

most citedReconstruction of Bandlimited Functions from Space-Time Samples

11 citations · 41 across the 16 of their papers we have counts for

collaborators

16 papers

math.FA2026

Bohr sets for multiplier algebras of complete Pick spaces

Ole Fredrik Brevig, Kristian Seip, Ilya Zlotnikov

We reexamine F. Wiener's classical proof that the Bohr radius of $H^{\infty}$ is $1/3$ . We replace $H^{\infty}$ by the multiplier algebras of complete Pick spaces and describe the Bohr…

math.CA2026

Asymptotic safety regions for Gabor frames generated by Hermite functions

Markus Faulhuber, Irina Shafkulovska, Ilya Zlotnikov

The aim of this paper is to establish new regions in the frame sets of Hermite functions $h_{n}$ . A classical result of Gröchenig and Lyubarskii shows that the Gabor system $\mathcal…

math.FA2026

Periodic Non-uniqueness Sets for Shift-invariant Spaces and Parity-Based Obstructions to the Frame Property for Gabor Systems

Alexander Ulanovskii, Ilya Zlotnikov

The goal of this note is twofold. First, we provide explicit examples of periodic (though not necessarily lattice) sets that give rise to Gabor systems failing to form frames. Our…

math.FA2026

Extreme and exposed points of shift-invariant spaces generated by Gaussian kernel and hyperbolic secant

Markus Valås Hagen, Alexander Ulanovskii, Denis Zelent +1

We characterize the extreme and exposed points of the unit ball (with respect to the $L^{1}$ -norm) in the shift-invariant space generated by the Gaussian function, as well as in the…

math.CV2025

Contractive Hardy--Littlewood inequalities in the Dirichlet range

Ole Fredrik Brevig, Aleksei Kulikov, Kristian Seip +1

The class $A_{α}^{p}$ consists of those analytic functions $f$ in the unit disc such that \[\|f\|_{α,p}^p := |f(0)|^p+\int_0^1 \left(\frac{d}{dr} M_p^p(r,f)\right) (1-r^2)^{α-1} \,dr <…

math.FA2024★ 1 cited

Stability of shifts, interpolation, and crystalline measures

Alexander Ulanovskii, Ilya Zlotnikov

Let $V_{Γ}^{p} (G), 1 \leq p \leq \infty,$ be the quasi shift-invariant space generated by $Γ$ -shifts of a function $G$ , where $Γ \subset R$ is a separated set. F…

math.FA2024★ 5 cited

Sampling in quasi shift-invariant spaces and Gabor frames generated by ratios of exponential polynomials

Alexander Ulanovskii, Ilya Zlotnikov

We introduce two families of generators (functions) $G$ that consist of entire and meromorphic functions enjoying a certain periodicity property and contain the classical…

math.FA2023★ 6 cited

Sampling in the shift-invariant space generated by the bivariate Gaussian function

José Luis Romero, Alexander Ulanovskii, Ilya Zlotnikov

We study the space spanned by the integer shifts of a bivariate Gaussian function and the problem of reconstructing any function in that space from samples scattered across the pla…

math.CA2022

Completeness of Certain Exponential Systems and Zeros of Lacunary Polynomials

Aleksei Kulikov, Alexander Ulanovskii, Ilya Zlotnikov

Let $Γ$ be a subset of ${0, 1, 2, ...}$ . We show that if $Γ$ has `gaps' then the completeness and frame properties of the system ${t^{k} e^{2 π in t} : n \in Z, k \in Γ}$ differ fro…

math.FA2022

Contractive projections in Paley-Wiener spaces

Aleksei Kulikov, Ilya Zlotnikov

Let $S_{1}$ and $S_{2}$ be disjoint finite unions of parallelepipeds. We describe necessary and sufficient conditions on the sets $S_{1}, S_{2}$ and exponents $p$ such that the canonical pr…

math.CA2021★ 2 cited

Sharp multiplicative inequalities with $BMO$ $II$

Vasily Vasyunin, Pavel Zatitskiy, Ilya Zlotnikov

We find the best possible constant $C$ in the inequality $∥ φ ∥_{L^{r}}^{\frac{p}{r}} \leq C ∥ φ ∥_{L^{p}}^{\frac{p}{r}} ∥ φ ∥_{BMO}^{1 - \frac{p}{r}}$ for all possible…

math.FA2021★ 1 cited

On geometry of the unit ball of Paley-Wiener space over two symmetric intervals

Alexander Ulanovskii, Ilya Zlotnikov

Let $P W_{S}^{1}$ be the space of integrable functions on $R$ whose Fourier transform vanishes outside $S$ , where $S = [- σ, - ρ] \cup [ρ, σ]$ , $0 < ρ < σ$ . In the case $ρ > σ /2$ , we prese…

math.CA2021★ 1 cited

On planar sampling with Gaussian kernel in spaces of bandlimited functions

Ilya Zlotnikov

Let $I = (a, b) \times (c, d) \subset R_{+}^{2}$ be an index set and let ${G_{α} (x)}_{α \in I}$ be a collection of Gaussian functions, i.e. $G_{α} (x) = exp (- α_{1} x_{1}^{2} - α_{2} x_{2}^{2})$ …

math.PR2021★ 4 cited

Sharp moment estimates for martingales with uniformly bounded square functions

Dmitriy Stolyarov, Vasily Vasyunin, Pavel Zatitskiy +1

We provide sharp bounds for the exponential moments and $p$ -moments, $1 ⩽ p ⩽ 2$ , of the terminate distribution of a martingale whose square function is uniformly bo…

math.CA2020★ 11 cited

Reconstruction of Bandlimited Functions from Space-Time Samples

Alexander Ulanovskii, Ilya Zlotnikov

For a wide family of even kernels ${φ_{u}, u \in I}$ , we describe discrete sets $Λ$ such that every bandlimited signal $f$ can be reconstructed from the space-time samples $\{(f\ast…

math.CA2020★ 10 cited

On 2-dimensional mobile sampling

Alexander Rashkovskii, Alexander Ulanovskii, Ilya Zlotnikov

Necessary and sufficient conditions are presented for several families of planar curves to form a set of stable sampling for the Bernstein space $B_{Ω}$ over a convex set $…

Bohr sets for multiplier algebras of complete Pick spaces

Asymptotic safety regions for Gabor frames generated by Hermite functions

Periodic Non-uniqueness Sets for Shift-invariant Spaces and Parity-Based Obstructions to the Frame Property for Gabor Systems

Extreme and exposed points of shift-invariant spaces generated by Gaussian kernel and hyperbolic secant

Contractive Hardy--Littlewood inequalities in the Dirichlet range

Stability of shifts, interpolation, and crystalline measures

Sampling in quasi shift-invariant spaces and Gabor frames generated by ratios of exponential polynomials

Sampling in the shift-invariant space generated by the bivariate Gaussian function

Completeness of Certain Exponential Systems and Zeros of Lacunary Polynomials

Contractive projections in Paley-Wiener spaces

Sharp multiplicative inequalities with BMO II

On geometry of the unit ball of Paley-Wiener space over two symmetric intervals

On planar sampling with Gaussian kernel in spaces of bandlimited functions

Sharp moment estimates for martingales with uniformly bounded square functions

Reconstruction of Bandlimited Functions from Space-Time Samples

On 2-dimensional mobile sampling

Sharp multiplicative inequalities with $BMO$ $II$