English

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

Analysis of PDEs 2023-01-06 v3 Spectral Theory

Abstract

We develop a set of LpL^{p} estimates for functions uu that are a joint quasimodes (approximate eigenfunctions) of rr semiclassical pseudodifferential operators p1(x,hD),,pr(x,hD)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.

Keywords

Cite

@article{arxiv.1804.02788,
  title  = {$L^{p}$ estimates for joint quasimodes of semiclassical pseudodifferential operators},
  author = {Melissa Tacy},
  journal= {arXiv preprint arXiv:1804.02788},
  year   = {2023}
}

Comments

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