Semiclassical<i>L</i><sup><i>p</i></sup>Estimates of Quasimodes on Submanifolds
Semiclassical<i>L</i><sup><i>p</i></sup>Estimates of Quasimodes on Submanifolds
Let P = P(h) be a semiclassical pseudodifferential operator on a Riemannian manifold M. Suppose that u(h) is a localized, L 2 normalized family of functions such that P(h)u(h) is O(h) in L 2, as h → 0. Then, for any submanifold Y ⊂ M, we obtain estimates on the …