S. Tikhonov

activity

20162026

collaborators

14 papers

math.CA2026

Fourier coefficients of continuous functions with sparse spectrum

Aleksei Kulikov, Miquel Saucedo, Sergey Tikhonov

Let $(r_{k})$ be an increasing sequence and $(w_{k})$ a positive sequence. We study the following question: is it true that for every sequence $(a_{k})$ satisfying $\sum_{k=0}^\infty |a_…

math.CA2026

A Logvinenko-Sereda theorem for lacunary spectra

Miquel Saucedo, Sergey Tikhonov

For a function $F$ represented as $F (x) = \sum_{n = 0}^{\infty} f_{n} (x) e^{2 π i λ_{n} x},$ where each $f_{n}$ satisfies $spec (f_{n}) \subset [0, 1]$ and $(λ_n)_{n\geq 0}\subset…

math.CA2026

Heisenberg's inequality in $L^{p}$

Miquel Saucedo, Sergey Tikhonov

In this paper, we obtain non-symmetric and symmetric versions of the classical Heisenberg-Pauli-Weyl uncertainty principle in Lebesgue spaces with power weights.

math.CA2025

Extremizers of a Fourier uncertainty principle related to averaging

Miquel Saucedo, Sergey Tikhonov

We study the uncertainty principle $∥ μ (ξ) ∣ ξ ∣^{β} ∥_{\infty}^{α} (\int ∣ x ∣^{α} d μ)^{β} \geq C (α, β, d) ∥ μ ∥_{T V}^{α + β}$ for finite non-negative measures…

math.CA2025

Kahane-Katznelson-de Leeuw theorem and absolute convergence of Fourier series

Miquel Saucedo, Sergey Tikhonov

We extend the Kahane-Katznelson-de Leeuw theorem to smoothness spaces by showing that for any $g \in W^{l, 2} (T^{d})$ , there exists a function $f \in C^{l} (T^{d})$ satisf…

math.CA2025

The Fourier transform is an extremizer of a class of bounded operators

Miquel Saucedo, Sergey Tikhonov

We show that, for a natural class of rearrangement admissible spaces $X$ and $Y$ , the Fourier operator is bounded between $X$ and $Y$ if and only if any operator of joint strong ty…

math.CA2024

Poisson summation formula in weighted Lebesgue spaces

Miquel Saucedo, Sergey Tikhonov

We characterize the parameters $(α, β, p, q)$ for which the condition $f ∣ x ∣^{α} \in L^{p}$ and $f ∣ ξ ∣^{β} \in L^{q}$ implies the validity of the Poisson summation formula, thus complet…

math.CA2024

Marcinkiewicz-Zygmund inequalities in quasi-Banach function spaces

Yurii Kolomoitsev, Sergey Tikhonov

We obtain Marcinkiewicz--ygmund (MZ) inequalities in various Banach and quasi-Banach spaces under minimal assumptions on the structural properties of these spaces. Our main results…

math.CA2024

Note on Fourier inequalities

Miquel Saucedo, Sergey Tikhonov

We prove that the Hausdorff--Young inequality $∥ f ∥_{q (\cdot)} \leq C ∥ f ∥_{p (\cdot)}$ with $q (x) = p^{'} (1/ x)$ and $p (\cdot)$ even and non-decreasing holds in variable…

math.FA2024

Sampling discretization in Orlicz spaces

Egor Kosov, Sergey Tikhonov

We obtain new sampling discretization results in Orlicz norms on finite dimensional spaces. As applications, we study sampling recovery problems, where the error of the recovery pr…

math.CA2024

Subcritical Fourier uncertainty principles

Miquel Saucedo, Sergey Tikhonov

It is well known that if a function $f$ satisfies $∥ f (x) e^{π α ∣ x ∣^{2}} ∥_{p} + ∥ f (ξ) e^{π α ∣ ξ ∣^{2}} ∥_{q} < \infty (*)$ with $α = 1$ and $1 \leq p, q < \infty$ , the…

math.CA2024

Bernstein-Nikolskii Inequality: Optimality with Respect to the Smoothness Parameter

Michael I Ganzburg, Miquel Saucedo, Sergey Tikhonov

In this paper, we study the form of the constant $C$ in the Bernstein--Nikolskii inequalities $∥ f^{(s)} ∥_{q} ≲ C (s, p, q) ∥ f ∥_{p}, 0 < p < q \leq \infty$ , for trigonom…

math.CA2023

Fourier inequalities in Morrey and Campanato spaces

Alberto Debernardi Pinos, Erlan Nursultanov, Sergey Tikhonov

We study norm inequalities for the Fourier transform, namely, \begin{equation}\label{introduction} \|\widehat f\|_{X_{p,q}^λ} \lesssim \|f\|_{Y}, \end{equation} where $X$ is either…

math.CA2016

Wiener's problem for positive definite functions

Dmitry Gorbachev, Sergey Tikhonov

We study the sharp constant $W_{n} (D)$ in Wiener's inequality for positive definite functions \[ \int_{\mathbb{T}^{n}}|f|^{2}\,dx\le W_{n}(D)|D|^{-1}\int_{D}|f|^{2}\,dx,\quad D\sub…

Fourier coefficients of continuous functions with sparse spectrum

A Logvinenko-Sereda theorem for lacunary spectra

Heisenberg's inequality in Lp

Extremizers of a Fourier uncertainty principle related to averaging

Kahane-Katznelson-de Leeuw theorem and absolute convergence of Fourier series

The Fourier transform is an extremizer of a class of bounded operators

Poisson summation formula in weighted Lebesgue spaces

Marcinkiewicz-Zygmund inequalities in quasi-Banach function spaces

Note on Fourier inequalities

Sampling discretization in Orlicz spaces

Subcritical Fourier uncertainty principles

Bernstein-Nikolskii Inequality: Optimality with Respect to the Smoothness Parameter

Fourier inequalities in Morrey and Campanato spaces

Wiener's problem for positive definite functions

Heisenberg's inequality in $L^{p}$