Semiclassical L-p Estimates of Quasimodes on Submanifolds

Tacy, Melissa

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Semiclassical L-p Estimates of Quasimodes on Submanifolds

Date

2010

Authors

Tacy, Melissa

Publisher

Marcel Dekker Inc.

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