13 citations · 42 across the 17 of their papers we have counts for
18 papers
Soliton and breather resolution for the cubic Szegö flow on the line
Patrick Gerard, Sandrine Grellier
We investigate the long time behaviour of the solutions of the cubic Szeg}o equation on the line in the Sobolev space H^{1/2}(R). We prove that, for every datum of which the Lax op…
Stein's theorem in the upper-half plane and Bergman spaces with weights
Aline Bonami, Sandrine Grellier, Benoît Sehba
This is a companion paper to our previous one, Avatars of Stein's Theorem in the complex setting. In this previous paper, we gave a sufficient condition for an integrable function…
Global Stein Theorem on Hardy spaces
Aline Bonami, Sandrine Grellier, Benoit Sehba
Let f be an integrable function which has integral 0 on R n. What is the largest condition on |f | that guarantees that f is in the Hardy space H 1 (R n)? When f is compactly suppo…
Turbulent cascades for a family of damped Szegö equations
Patrick Gérard, Sandrine Grellier, Zihui He
In this paper, we study the transfer of energy from low to high frequencies for a family of damped Szegö equations. The cubic Szegö equation has been introduced as a toy model for…
On a damped Szego equation (with an appendix in collaboration with Christian Klein)
Patrick Gerard, Sandrine Grellier
We investigate how damping the lowest Fourier mode modifies the dynamics of the cubic Szeg{ö} equation. We show that there is a nonempty open subset of initial data generating traj…
Generic colourful tori and inverse spectral transform for Hankel operators
Patrick Gerard, Sandrine Grellier
This paper explores the regularity properties of an inverse spectral transform for Hilbert--Schmidt Hankel operators on the unit disc. This spectral transform plays the role of act…