$L^{p}$ estimates for joint quasimodes of semiclassical pseudodifferential operators

Melissa Tacy

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arXiv · 1804.02788

$L^{p}$ estimates for joint quasimodes of semiclassical pseudodifferential operators

Melissa Tacy

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Abstract

We develop a set of $L^{p}$ estimates for functions $u$ that are a joint quasimodes (approximate eigenfunctions) of $r$ semiclassical pseudodifferential operators $p_{1}(x,hD),\dots,p_{r}(x,hD)$. This work extends Sarnak and Marshall's work on symmetric space to cover a more general class of manifolds/operators.

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Melissa Tacy. 2018-04-09. $L^{p}$ estimates for joint quasimodes of semiclassical pseudodifferential operators. https://arxiv.org/abs/1804.02788

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