Semiclassical L-p Estimates of Quasimodes on Submanifolds

Abstract

Let P = P(h) be a semiclassical pseudodifferential operator on a Riemannian manifold M. Suppose that u(h) is a localized, L2 normalized family of functions such that P(h)u(h) is O(h) in L2, as h → 0. Then, for any submanifold Y ⊂ M, we obtain estimate Show more