Improved spectral projection estimates

2022/11/30 by Blair, Matthew D., Huang, Xiaoqi, Sogge, Christopher D. · 1 citation
#35 #58 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2211.17266

Abstract

We obtain new improved spectral projection estimates on manifolds of non-positive curvature, including sharp ones for relatively large spectral windows for general tori. Our results are stronger than those in an earlier work of the first and third authors [6], and the arguments have been greatly simplified. We more directly make use of pointwise estimates that are implicit in the work of Berard [2] and avoid the use of weak-type spaces that were used in the previous works [6] and [22]. We also simplify and strengthen the bilinear arguments by exploiting the use of microlocal L²→ L^q_c Kakeya-Nikodym estimates and avoiding the of L²→ L² ones as in earlier results. This allows us to prove new results for manifolds of negative curvature and some new sharp estimates for tori. We also have new and improved techniques in two dimensions for general manifolds of non-positive curvature.

Cited by

• Sharp microlocal Kakeya--Nikodym estimates for eigenfunctions with applications

Related

• Sharp Spectral Projection Estimates for the Torus at p_c=(2(n+1))/(n-1)
• Curvature and sharp growth rates of log-quasimodes on compact manifolds
• Spectral projection estimates restricted to uniformly embedded submanifolds
• Lossless Strichartz and spectral projection estimates on unbounded manifolds
• Propagation of smallness and spectral estimates