arXiv subjects

Marcu-Antone Orsoni

Publications and source records attributed to Marcu-Antone Orsoni.

8 recordsLinked to original sources

arXiv2026

Fourier decay of Gaussian multiplicative chaos and boundary geometry

In this paper, we develop a new approach to studying the Fourier transform of Gaussian multiplicative chaos. We determine the Fourier dimension of these random measures on tori for every smooth log-correlated covariance and in every dimension, and prove sharp bounds and exact formulas for chaos on natural classes of bounded sets and hypersurfaces in Euclidean space. These results highlight how boundary geometry and multifractal concentration jointly govern Fourier decay, including regimes in which the boundary strictly reduces the Fourier dimension. In the circle setting, this gives a substantially simpler new proof of a conjecture of Garban and Vargas.

math.PR↗

arXiv2026

Identifying Bergman space functions from intervals

We characterize functions of a Bergman space on a square by their values and derivatives on the diagonals. This problem is connected with the reachable space of the one-dimensional heat equation on a finite interval with boundary $L^2$-controls.

math.CV↗

arXiv2024

On the dimension of observable sets for the heat equation

We consider the heat equation on a bounded $C^1$ domain in $\mathbb{R}^n$ with Dirichlet boundary conditions. The primary aim of this paper is to prove that the heat equation is observable from any measurable set with a Hausdorff dimension strictly greater than $n - 1$. The proof relies on a novel spectral estimate for linear combinations of Laplace eigenfunctions, achieved through the propagation of smallness for solutions to Cauchy-Riemann systems as established by Malinnikova, and uses the Lebeau-Robbiano method. While this observability result is sharp regarding the Hausdorff dimension scale, our secondary goal is to construct families of sets with dimensions less than $n - 1$ from which the heat equation is still observable.

math.AP↗

arXiv2023

Sampling constants in generalized Fock spaces

We prove several results related to a Logvinenko-Sereda type theorem on dominating sets for generalized doubling Fock spaces. In particular, we give a precise polynomial dependence of the sampling constant on the relative density parameter $γ$ of the dominating set. Our method is an adaptation of that used in \cite{HKO} for the Bergman spaces and is based on a Remez-type inequality and a covering lemma related to doubling measures.

math.CA↗

arXiv2021

Reachable space of the Hermite heat equation with boundary control

We discuss reachable states for the Hermite heat equation on a segment with boundary $L^2$-controls. The Hermite heat equation corresponds to the heat equation to which a quadratic potential is added. We will discuss two situations: when one endpoint of the segment is the origin and when the segment is symmetric with respect to the origin. One of the main results is that reachable states extend to functions in a Bergman space on a square one diagonal of which is the segment under consideration, and that functions holomorphic in a neighborhood of this square are reachable.

math.AP↗

arXiv2021

Separation of singularities for the Bergman space and application to control theory

In this paper, we solve a separation of singularities problem in the Bergman space. More precisely, we show that if $P\subset \mathbb{C}$ is a convex polygon which is the intersection of $n$ half planes, then the Bergman space on $P$ decomposes into the sum of the Bergman spaces on these half planes. The result applies to the characterization of the reachable space of the one-dimensional heat equation on a finite interval with boundary controls. We prove that this space is a Bergman space of the square which has the given interval as a diagonal. This gives an affirmative answer to a conjecture raised in [HKT20].

math.AP↗

arXiv2020

Dominating sets in Bergman spaces and sampling constants

We discuss sampling constants for dominating sets in Bergman spaces. Our method is based on a Remez-type inequality by Andrievskii and Ruscheweyh. We also comment on extensions of the method to other spaces such as Fock and Paley-Wiener spaces.

math.CA↗

arXiv2019

Reachable states and holomorphic function spaces for the 1-D heat equation

The description of the reachable states of the heat equation is one of the central questions in control theory. The aim of this work is to present new results for the 1-D heat equation with boundary control on the segment $[0, π]$. In this situation it is known that the reachable states are holomorphic in a square $D$ the diagonal of which is given by $[0,π]$. The most precise results obtained recently say that the reachable space is contained between two well known spaces of analytic function: the Smirnov space $E^2(D)$ and the Bergman space $A^2(D)$. We show that the reachable states are exactly the sum of two Bergman spaces on sectors the intersection of which is $D$. In order to get a more precise information on this sum of Bergman spaces, we also prove that it includes the Smirnov-Zygmund space $E_{L\log^+\!L}(D)$ as well as a certain weighted Bergman space on $D$.

math.AP↗