arXiv subjects

Quentin Rible

Publications and source records attributed to Quentin Rible.

3 recordsLinked to original sources

arXiv2026

Traces of functions in Besov spaces in Gibbs environment

This paper investigates the traces of functions belonging to the inhomogeneous Besov spaces B $\xi$ p,q , where $\xi$ is a product of capacities defined as powers of Gibbs measures. We first establish that the traces of functions in B $\xi$ p,q along affine hyperplanes belong to another inhomogeneous Besov space. Furthermore, we derive an upper bound for the singularity spectrum of the traces of all functions in B $\xi$ $\infty$,q . This bound is then refined for a prevalent set of functions in B $\xi$ $\infty$,q , for which we explicitly compute the singularity spectrum of their traces. Notably, our analysis reveals that the regularity properties of these affine traces are highly sensitive to the choice of the hyperplane along which the trace is taken.

math.FA↗

arXiv2026

A non-vanishing property for tensor products of wavelets

We prove that, given a wavelet $\psi$, it is possible to choose some multi-integers $(p_j=(p_{j,1},...,p_{j,d}))_{j \in \mathbb{Z}} \in \mathbb{Z}^d$ such that, for every $x=(x_1,...,x_d) \in \mathbb{R}^d$, for infinitely many integers $j$, the tensorized wavelet $\prod_{i=1}^d \psi(2^j x_i-p_{j,i})$ does not vanish at $x$. This non-vanishing property is essential for analyzing some generic regularity properties in certain Sobolev and Besov spaces. The proof relies on an assumption regarding the zeros of $\psi$, which we numerically verify for the first Daubechies wavelets.

math.FA↗

arXiv2025

Inhomogeneous Sobolev and Besov Spaces: Embeddings and prevalent smoothness

In this article, we introduce inhomogeneous Sobolev spaces that naturally generalise the standard Sobolev-Slobodeckij spaces. The inhomogeneity of these spaces is governed by a set function $\mu$, referred to as an environment. In the case where $\mu$ is an almost doubling set function, we relate these new spaces with inhomogeneous Besov spaces recently introduced by Barral-Seuret in 2023. When $\mu$ is in addition a capacity, wee also prove that prevalent elements in such spaces are multifractal (with a singularity spectrum that we determine), completing previous Baire generic results already obtained.

math.CA↗