Semiclassical $L^p$ restriction quasimode estimates in two dimensions
Semiclassical $L^p$ restriction quasimode estimates in two dimensions
Consider a 2-dimensional smooth Riemannian manifold $M$, and let $P(h)$ be a semiclassical pseudodifferential operator on $M$. Assume that $f = f(h)$ is an $O(h)$ quasimode of $P(h)$ localized in phase space. In this work, we establish sharp $L^p$ restriction estimates for quasimodes for all smooth curves in two dimensions. …