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

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.

arXiv commentMajor theorems remain the same as V2. Curvature conditions has been relaxed (see the discussion in Section 2). This is the final version