Semiclassical L^p quasimode restriction estimates in two dimensions

2024/01/30 by Oh, Sewook, Ryu, Jaehyeon
#35PXX #35SXX #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2401.16881

Abstract

We establish the L^p restriction estimates for quasimodes on a smooth curve in two dimensions. Our estimates are sharp for all smooth curves. As an application, we address L^p eigenfunction restriction estimates for Laplace-Beltrami eigenfunctions on 2-dimensional compact Riemannian manifolds without boundary and Hermite functions on \mathbb R². Our method involves a geometric analysis of the contact order between the curve and the bicharacteristic flow of the semiclassical pseudodifferential operator.

Related

• Lp bilinear quasimode estimates
• Refined L^p restriction estimate for eigenfunctions on Riemannian surfaces
• Eigenfunctions restriction estimates for curves with nonvanishing geodesic curvatures in compact Riemannian surfaces with nonpositive curvature
• Restrictions of the Laplace-Beltrami eigenfunctions to submanifolds
• L^p estimates for joint quasimodes of two pseudodifferential operators whose characteristic sets have k-th order contact