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

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6 papers · 1 filter

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.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.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.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.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 $…