163 citations · 514 across the 46 of their papers we have counts for
56 papers
L2 to Lp bounds for spectral projectors on thin intervals in Riemannian manifolds
Pierre Germain
Given a Riemannian manifold endowed with its Laplace-Beltrami operator, consider the associated spectral projector on a thin interval. As an operator from L2 to Lp, what is its ope…
Spectral projectors on hyperbolic surfaces
Jean-Philippe Anker, Pierre Germain, Tristan Léger
In this paper, we prove estimates, where , for spectral projectors on a wide class of hyperbolic surfaces. More precisely, we consider projections in small spect…
Asymptotic Stability of Solitary Waves for One Dimensional Nonlinear Schrödinger Equations
Charles Collot, Pierre Germain
We show global asymptotic stability of solitary waves of the nonlinear Schrödinger equation in space dimension 1. Furthermore, the radiation is shown to exhibit long range scatteri…
Stability and cascades for the Kolmogorov-Zakharov spectrum of wave turbulence
Charles Collot, Helge Dietert, Pierre Germain
The kinetic wave equation arises in wave turbulence to describe the Fourier spectrum of solutions to the cubic Schroedinger equation. The equation has two Kolmogorov-Zakharov stead…
Bounds for spectral projectors on generic tori
Pierre Germain, Simon L. Rydin Myerson
We investigate norms of spectral projectors on thin spherical shells for the Laplacian on generic tori, including generic rectangular tori. We state a conjecture and partially prov…
Bounds for spectral projectors on the Euclidean cylinder
Pierre Germain, Simon L. Rydin Myerson
We prove essentially optimal bounds for norms of spectral projectors on thin spherical shells for the Laplacian on the cylinder (R/Z)*R. In contrast to previous investigations into…