arXiv subjects

Vincent Munnier

Publications and source records attributed to Vincent Munnier.

5 recordsLinked to original sources

arXiv2026

Common frequently hypercyclic random vectors

We study common frequently hypercyclic vectors for countable families of weighted backward shifts acting on $\ell_p$ spaces, $1\leq p<\infty$. Using probabilistic techniques, we develop a general existence criterion, complemented by a non-existence result. These insights are then applied to the specific setting of countable families of polynomials of weighted backward shifts, providing conditions under which they share a common frequently hypercyclic vector.

math.FA↗

arXiv2025

Optimal growth of upper frequently hypercyclic functions for some weighted Taylor shifts

We are interested in the optimal growth in terms of $L^p$-averages of hypercyclic and $\mathcal{U}$-frequently hypercyclic functions for some weighted Taylor shift operators acting on the space of analytic function on the unit disc. We unify the results obtained by considering intermediate notions of upper frequent hypercyclicity between the $\mathcal{U}$-frequent hypercyclicity and the hypercyclicity.

math.CA↗

arXiv2024

Marcinkiewicz Type Theorems for Interpolation of Operators Acting on M{ü}ntz Spaces

We prove interpolation results in the spirit of the Marcinkiewicz theorem. The operators considered in this article are defined on Müntz spaces, which are not dense subspaces of $L^p$, and for which the classical interpolation theory cannot be applied directly. Our proofs crucially rely on strong decoupling of $L^p$ norms, a that was first observed by Gurariy-Macaev and later generalized.

math.FA↗

arXiv2024

Generalized Carleson Embeddings of M{ü}ntz Spaces

This paper establishes Carleson embeddings of M{ü}ntz spaces $M^q_Λ$ into weighted Lebesgue spaces $L^p(\mathrm{d}μ)$, where $μ$ is a Borel regular measure on $[0,1]$ satisfying $μ([1-\varepsilon])\lesssim \varepsilon^β$. In the case $β\geqslant 1$ we show that such measures are exactly the ones for which Carleson embeddings $L^{\frac{p}β} \hookrightarrow L^p(\mathrm{d}μ)$ hold. The case $β\in (0,1)$ is more intricate but we characterize such measures $μ$ in terms of a summability condition on their moments. Our proof relies on a generalization of $L^p$ estimates {à} la Gurariy-Macaev in the weighted $L^p$ spaces setting, which we think can be of interest in other contexts.

math.CA↗

arXiv2014

Generalized universal series

We unify the recently developed abstract theories of universal series and extended universal series to include sums of the form $\sum_{k=0}^n a_k x_{n,k}$ for given sequences of vectors $(x_{n,k})_{n\geq k\geq 0}$ in a topological vector space X. The algebraic and topological genericity as well as the spaceability are discussed. Then we provide various examples of such generalized universal series which do not proceed from the classical theory. In particular, we build universal series involving Bernstein's polynomials, we obtain a universal series version of MacLane's Theorem, and we extend a result of Tsirivas concerning universal Taylor series on simply connected domains, exploiting Bernstein- Walsh quantitative approximation theorem.

math.FA↗