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New files
Integrals of the Wigner distribution on Higher Dimensional Cones,
(41 pages),
Annali dell' Universitá di Ferrara, 72,
4, August
(2026).
We study integrals of the Wigner distribution on higher dimensional cones of the phase space. We show in particular that there are very simple examples of cones of the phase space
ℝ2n, with n ≥2, on which the integral of the Wigner distribution of a pulse in L2(ℝn) does not converge. It is a sharp contrast with the case n=1,
in which we are able to calculate explicitly the integral of the Wigner distribution
on all cones of the phase space ℝ2.
DOI number: https://doi.org/10.1007/s11565-026-00734-0, link on HAL.
Wiener Algebras Methods for Liouville theorems on the stationary Navier-Stokes system,
(67 pages), January 20 (2026),
file on arXiv.
We prove some Liouville theorems for the stationary Navier-Stokes system for incompressible fluids.
We provide some sufficient conditions on the low frequency part of the solution,
using some properties of classical singular integrals with respect to Wiener algebras.
The reader will find a few words of introduction to this preprint in the pdf file
Introductory words.
Here is a
video-link
to the you-tube channel of the LJLL,
where the slides of a talk on this topic can be found.
link on HAL.
Symplectic, Metaplectic Groups and Integrals of the Wigner Distribution,
(69 pages),
Pure and Applied Functional Analysis
,
Volume 10
(dedicated to Professor Gilles Godefroy on the occasion of his 70th birthday), Number 4, (2025), 875-943.
We are interested in the developments of recent results on integrals of the Wigner distribution on subsets of the phase space. We begin with an elementary introduction to the symplectic and metaplectic groups,
proceeding afterwards to the signal theory topics linked to the Wigner distribution.
Along our way, we emphasize the link between Quantum Mechanics with the Weyl quantization and Signal Theory questions involving the Wigner distribution.
DOI number: --,
link on HAL.
On the Uncertainty Principle for Metaplectic Transformations,
(59 pages),
Journal of Functional Analysis,
Volume 289, Issue 5, 1 September 2025, 110997.
We explore the new proofs and extensions of the Heisenberg Uncertainty Principle introduced by A. Widgerson & Y. Widgerson in [MR4229152], developed in [MR4453622] by N.C. Dias, F. Luef and J.N. Prata and also in [MR4337266] by Y. Tang. In particular we give here a proof of the Uncertainty Principle for operators in the Metaplectic group in any dimension.
DOI number: https://doi.org/10.1016/j.jfa.2025.110997,
link on HAL.
On Some Singular Integrals Linked to Solvability and Signal Theory,
an article (pages 225 to 276)
in the book
Geometric Analysis of PDEs and Several Complex Variables
In Honor of Jorge Hounie's 75th Birthday,
edited by
S. Berhanu, N.Mir, G.Hoepfner,
published in 2024
in the Springer-Verlag Latin American Mathematics Series.
We explore in this paper the role of some singular integrals in the disproof of some estimates linked to solvability properties of pseudo-differential equations; it turns out that some of these singular integrals are also related to the construction of a counterexample to Flandrin's conjecture in signal theory.
DOI number: 10.1007/978-3-031-69702-9,
link on HAL.
updated
September 15, 2026
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