A. Kulikov

activity

20182025

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4 papers · 1 filter

math.CA2023

Fourier uniqueness and non-uniqueness pairs

Aleksei Kulikov, Fedor Nazarov, Mikhail Sodin

Motivated by recent works by Radchenko and Viazovska and by Ramos and Sousa, we find sufficient conditions for a pair of discrete subsets of the real line to be a uniqueness or a n…

math.CA2023

Exponential lower bound for the eigenvalues of the time-frequency localization operator before the plunge region

Aleksei Kulikov

We prove that the eigenvalues $λ_{n} (c)$ of the time-frequency localization operator satisfy $λ_{n} (c) > 1 - δ^{c}$ for $n = [(1 - ε) c]$ , where $δ = δ (ε) < 1$ and $\vare…

math.CA2020

Fourier interpolation and time-frequency localization

Aleksei Kulikov

We prove that under very mild conditions for any interpolation formula $f (x) = \sum_{λ \in Λ} f (λ) a_{λ} (x) + \sum_{μ \in M} f^(μ) b_{μ} (x)$ we have a lower bound for the counting fun…

math.CA2020

A contractive Hardy-Littlewood inequality

Aleksei Kulikov

We prove a contractive Hardy-Littlewood type inequality for functions from $H^{p} (T)$ , $0 < p \leq 2$ which is sharp in the first two Taylor coefficients and asymptotically a…