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arXiv · 0905.2240

Semiclassical L^p Estimates of Quasimodes on Submanifolds

Melissa Tacy
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Abstract

Let M be a compact manifold and P = P(h) a semiclassical pseudodifferential operator on M . Suppose that u(h) is a L^2 normalised family of functions such that P(h)u(h) is O(h) in L^2, as h goes to 0. Then, for any compact submanifold Y contained in M, we obtain estimates on the L^p norm of u(h) restricted to Y, with exponents that are sharp for h goes to 0. As part of the technical development we prove some extensions of the abstract Strichartz estimates of Keel and Tao.

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Melissa Tacy. 2009-05-14. Semiclassical L^p Estimates of Quasimodes on Submanifolds. https://arxiv.org/abs/0905.2240

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