Lp bilinear quasimode estimates

2015/03/02 by Guo, Zihua, Han, Xiaolong, Tacy, Melissa
#Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1503.00413

Abstract

In this paper, we investigate the L^p bilinear quasimode estimates on compact Riemannian manifolds. We obtain results in the full range p≥2 on all n-dimensional manifolds with n≥2. This in particular implies the L^p bilinear eigenfunction estimates. We further show that all of these estimates are sharp by constructing various quasimodes and eigenfunctions that saturate our estimates.

Related

• Semiclassical L^p quasimode restriction estimates in two dimensions
• Approximating Pointwise Products of Quasimodes
• Curvature and harmonic analysis on compact manifolds
• Quasimode concentration on compact space forms
• Multilinear eigenfunction estimates for the Laplace spectral projectors on compact manifolds