S. Tikhonov

activity

20242026

collaborators

9 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 $F (x) = \sum_{n = 0}^{\infty} f_{n} (x) e^{2 I ¨ i I^»_{n} x},$ where each $f_{n}$ satisfies $spec (f_{n}) \subset [0, 1]$ and $(Î»_n)_{n\geq 0}\sub…

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 $∥ I^¼ (I^¾) ∣ I^¾ ∣^{2} ∥_{\infty}^{I^} \pm (\int ∣ x ∣^{I^} \pm d I^¼)^{2} \geq C (I^\pm, I^^{2}, d) ∥ I^¼ ∥_{T V}^{I^\pm+ I^^{2}}$ for finite non-nega…

math.CA2025

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.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…

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

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

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

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