F. Bayart

activity

20022024

most citedDifference sets and frequently hypercyclic weighted shifts

70 citations · 262 across the 32 of their papers we have counts for

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32 papers · 1 filter

math.FA2024

Hereditarily frequently hypercyclic operators and disjoint frequent hypercyclicity

F. Bayart, S. Grivaux, E. Matheron +1

We introduce and study the notion of hereditary frequent hypercyclicity, which is a reinforcement of the well known concept of frequent hypercyclicity. This notion is useful for th…

math.FA2023

Essential norms of composition operators and multipliers acting between different Hardy spaces

Frédéric Bayart

We compute the essential norm of inclusion operators, composition operators and multipliers acting from a closed subspace of some $L^{p}$ -space into a subspace of some $L^{q}$ -space, w…

math.FA2023★ 2 cited

Schatten class composition operators on the Hardy space of Dirichlet series and a comparison-type principle

Frédéric Bayart, Athanasios Kouroupis

We give necessary and sufficient conditions for a composition operator with Dirichlet series symbol to belong to the Schatten classes $S_{p}$ of the Hardy space $H^{2}$ of Di…

math.FA2023

$ε$ -hypercyclic operators that are not $δ$ -hypercyclic for $δ$ < $ε$

Frédéric Bayart

For every fixed $ε$ $\in$ (0, 1), we construct an operator on the separable Hilbert space which is $δ$ -hypercyclic for all $δ$ $\in$ ( $ε$ , 1) and which is not $δ$ -hypercyclic for a…

math.FA2022

Disjoint frequent hypercyclicity of composition operators

Frédéric Bayart

We give a sufficient condition for two operators to be disjointly frequently hypercyclic. We apply this criterion to composition operators acting on $H (D)$ or on the Hardy…

math.FA2022

Cyclicity of composition operators on the Fock space

Frédéric Bayart, Sebastián Tapia-García

In this paper we provide a full characterization of cyclic composition operators defined on the d-dimensional Fock space $F (C^{d})$ in terms of their symbol. Also, w…

math.FA2022

Universality of general Dirichlet series with respect to translations and rearrangements

Frédéric Bayart

We give sufficient conditions for a general Dirichlet series to be universal with respect to translations or rearrangements.

math.FA2021★ 4 cited

Counting functions for Dirichlet series and compactness of composition operators

Frédéric Bayart

We give a sufficient condition for a composition operator with positive characteristic to be compact on the Hardy space of Dirichlet series.

math.FA2021★ 1 cited

Topological structure of the space of composition operators on the Hardy space of Dirichlet series

Frédéric Bayart, Maofa Wang, Xingxing Yao

The aim of this paper is to study when two composition operators on the Hilbert space of Dirichlet series with square summable coefficients belong to the same component or when the…

math.FA2021

Common hypercyclic vectors and dimension of the parameter set

Frédéric Bayart, Fernando Costa, Quentin Menet

We investigate the existence of a common hypercyclic vector for a family $(T_{λ})_{λ \in Λ}$ of hypercyclicoperators acting on the same Banach space $X$ . We give positive and negative…

math.FA2021★ 8 cited

Convergence and almost sure properties in Hardy spaces of Dirichlet series

Frédéric Bayart

Given a frequency $λ$ , we study general Dirichlet series $\sum a_{n} e^{- λ_{n} s}$ . First, we give a new condition on $λ$ which ensures that a somewhere convergent Dirichlet series def…

math.FA2021

Two problems on weighted shifts in linear dynamics

Frédéric Bayart

We show that an invertible bilateral weighted shift is strongly structurally stable if and only if it has the shadowing property. We also exhibit a K{ö}the sequence space supportin…

math.FA2019

Baire theorem and hypercyclic algebras

Frédéric Bayart, Fernando Costa Júnior, Dimitris Papathanasiou

The question of whether a hypercyclic operator $T$ acting on a Fr{é}chet algebra $X$ admits or not an algebra of hypercyclic vectors (but 0) has been addressed in the recent litera…

math.FA2019

Composition operators on spaces of double Dirichlet series

Frédéric Bayart, Jaime Castillo-Medina, Domingo García +2

We study composition operators on spaces of double Dirichlet series, focusing our interest on the characterization of the composition operators of the space of bounded double Diric…

math.FA2018★ 1 cited

On coincidence results for summing multilinear operators: interpolation, $ℓ_{1}$ -spaces and cotype

F. Bayart, D. Pellegrino, P. Rueda

Grothendieck's theorem asserts that every continuous linear operator from $ℓ_{1}$ to $ℓ_{2}$ is absolutely $(1, 1)$ -summing. This kind of result is commonly called coincidence res…

math.FA2018

Hypercyclic algebras

Frédéric Bayart

We prove the existence of algebras of hypercyclic vectors in three cases: convolution operators, composition operators, and backward shift operators.

math.FA2018

Convergence and divergence of wavelet series: multifractal aspects

Frédéric Bayart

We study the convergence and divergence of the wavelet expansion of a function in a Sobolev or a Besov space from a multifractal point of view. In particular, we give an upper boun…

math.FA2017

Multiple summing mpas : coordinatewise summability, inclusion theorems and p-Sidon sets

Frédéric Bayart

We discuss the multiple summability of a multilinear map $T : X_{1} \times \dots \times X_{m} \to Y$ when we have informations on the summability of the maps it induces on each coordinate.…

math.FA2017★ 14 cited

Contractive inequalities for Bergman spaces and multiplicative Hankel forms

Frédéric Bayart, Ole Fredrik Brevig, Antti Haimi +2

We consider sharp inequalities for Bergman spaces of the unit disc, establishing analogues of the inequality in Carleman's proof of the isoperimetric inequality and of Weissler's i…

math.FA2016

Monomial convergence for holomorphic functions on $ℓ_r$

Frédéric Bayart, Andreas Defant, Sunke Schlüters

Let $F$ be either the set of all bounded holomorphic functions or the set of all $m$ -homogeneous polynomials on the unit ball of $ℓ_r$ . We give a systematic study of t…

math.FA2015★ 9 cited

Compact composition operators with non-linear symbols on the $H^{2}$ space of Dirichlet series

Frédéric Bayart, Ole Fredrik Brevig

We investigate the compactness of composition operators on the Hardy space of Dirichlet series induced by a map $φ (s) = c_{0} s + φ_{0} (s)$ , where $φ_{0}$ is a Dirichlet polynomial. Our resul…

math.FA2015★ 4 cited

Common hypercyclic vectors for high dimensional families of operators

Frédéric Bayart

Let $(T_λ)_λ \in Λ$ be a family of operators acting on a $F$ -space $X$ , where the parameter space $Λ$ is a subset of $R^{d}$ . We give sufficient conditions on the family to…

math.FA2014★ 52 cited

Multipliers of Dirichlet series and monomial series expansions of holomorphic functions in infinitely many variables

Frédéric Bayart, Andreas Defant, Leonhard Frerick +2

Let $H_{\infty}$ be the set of all ordinary Dirichlet series $D = \sum_{n} a_{n} n^{- s}$ representing bounded holomorphic functions on the right half plane. A multiplicative sequ…

math.FA2013★ 5 cited

Optimal Hardy-Littlewood type inequalities for polynomials and multilinear operators

Nacib Albuquerque, Frédéric Bayart, Daniel Pellegrino +1

In this paper we obtain quite general and definitive forms for Hardy-Littlewood type inequalities. Moreover, when restricted to the original particular cases, our approach provides…

Hereditarily frequently hypercyclic operators and disjoint frequent hypercyclicity

Essential norms of composition operators and multipliers acting between different Hardy spaces

Schatten class composition operators on the Hardy space of Dirichlet series and a comparison-type principle

ε-hypercyclic operators that are not δ-hypercyclic for δ < ε

Disjoint frequent hypercyclicity of composition operators

Cyclicity of composition operators on the Fock space

Universality of general Dirichlet series with respect to translations and rearrangements

Counting functions for Dirichlet series and compactness of composition operators

Topological structure of the space of composition operators on the Hardy space of Dirichlet series

Common hypercyclic vectors and dimension of the parameter set

Convergence and almost sure properties in Hardy spaces of Dirichlet series

Two problems on weighted shifts in linear dynamics

Baire theorem and hypercyclic algebras

Composition operators on spaces of double Dirichlet series

On coincidence results for summing multilinear operators: interpolation, ℓ1​-spaces and cotype

Hypercyclic algebras

Convergence and divergence of wavelet series: multifractal aspects

Multiple summing mpas : coordinatewise summability, inclusion theorems and p-Sidon sets

Contractive inequalities for Bergman spaces and multiplicative Hankel forms

Monomial convergence for holomorphic functions on ℓ_r

Compact composition operators with non-linear symbols on the H2 space of Dirichlet series

Common hypercyclic vectors for high dimensional families of operators

Multipliers of Dirichlet series and monomial series expansions of holomorphic functions in infinitely many variables

Optimal Hardy-Littlewood type inequalities for polynomials and multilinear operators

$ε$ -hypercyclic operators that are not $δ$ -hypercyclic for $δ$ < $ε$

On coincidence results for summing multilinear operators: interpolation, $ℓ_{1}$ -spaces and cotype

Monomial convergence for holomorphic functions on $ℓ_r$

Compact composition operators with non-linear symbols on the $H^{2}$ space of Dirichlet series