Zobrazeno 1 - 10
of 87
pro vyhledávání: '"Grellier, Sandrine"'
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 supported, it is well-known that it is necessary and sufficient that |f | b
Externí odkaz:
http://arxiv.org/abs/2209.03595
In this paper, we study the transfer of energy from low to high frequencies for a family of damped Szeg\"o equations. The cubic Szeg\"o equation has been introduced as a toy model for a totally non-dispersive degenerate Hamiltonian equation. It is a
Externí odkaz:
http://arxiv.org/abs/2111.05247
Autor:
Gerard, Patrick, Grellier, Sandrine
We investigate how damping the lowest Fourier mode modifies the dynamics of the cubic Szeg{\"o} equation. We show that there is a nonempty open subset of initial data generating trajec-tories with high Sobolev norms tending to infinity. In addition,
Externí odkaz:
http://arxiv.org/abs/1912.10933
Autor:
Gerard, Patrick, Grellier, Sandrine
Publikováno v:
Tunisian J. Math. 1 (2019) 347-372
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 action-angles variables for an integrable infinite dimensional Hamiltonia
Externí odkaz:
http://arxiv.org/abs/1712.02073
We give an atomic decomposition of closed forms on R n , the coefficients of which belong to some Hardy space of Musielak-Orlicz type. These spaces are natural generalizations of weighted Hardy-Orlicz spaces, when the Orlicz function depends on the s
Externí odkaz:
http://arxiv.org/abs/1601.03856
Autor:
Grellier, Sandrine, Gerard, Patrick
This monograph is an expanded version of the preprint arXiv:1402.1716 or hal-00943396v1.It is devoted to the dynamics on Sobolev spaces of the cubic Szeg{\"o} equation on the circle ${\mathbb S} ^1$,$$ i\partial \_t u=\Pi (\vert u\vert ^2u)\ .$$Here
Externí odkaz:
http://arxiv.org/abs/1508.06814
Autor:
Gerard, Patrick, Grellier, Sandrine
The goal of this paper is to construct a nonlinear Fourier transformation on the space of symbols of compact Hankel operators on the circle. This transformation allows to solve a general inverse spectral problem involving singular values of a compact
Externí odkaz:
http://arxiv.org/abs/1402.1716
Autor:
Gérard, Patrick, Grellier, Sandrine
We derive an explicit formula for the general solution of the cubic Szeg\"o equation and of the evolution equation of the corresponding hierarchy. As an application, we prove that all the solutions corresponding to finite rank Hankel operators are qu
Externí odkaz:
http://arxiv.org/abs/1304.2619
Autor:
Gerard, Patrick, Grellier, Sandrine
Given two arbitrary sequences $(\lambda_j)_{j\ge 1}$ and $(\mu_j)_{j\ge 1}$ of real numbers satisfying $$|\lambda_1|>|\mu_1|>|\lambda_2|>|\mu_2|>...>| \lambda_j| >| \mu_j| \to 0\ ,$$ we prove that there exists a unique sequence $c=(c_n)_{n\in\Z_+}$,
Externí odkaz:
http://arxiv.org/abs/1201.4971
Autor:
Gerard, Patrick, Grellier, Sandrine
We consider the following degenerate half wave equation on the one dimensional torus $$\quad i\partial_t u-|D|u=|u|^2u, \; u(0,\cdot)=u_0. $$ We show that, on a large time interval, the solution may be approximated by the solution of a completely int
Externí odkaz:
http://arxiv.org/abs/1110.5719