Miquel Saucedo · wovepaper

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20242026

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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_…

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…

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.

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…

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…

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…

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…

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…

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…

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…