$L^p$ estimates for joint quasimodes of two pseudodifferential operators whose characteristic sets have $k$-th order contact

Madelyne M. Brown; Melissa Tacy

$L^p$ estimates for joint quasimodes of two pseudodifferential operators whose characteristic sets have $k$-th order contact

Analysis of PDEs 2025-04-11 v1

Authors: Madelyne M. Brown , Melissa Tacy

Abstract

On a smooth, compact, $n$ -dimensional Riemannian manifold, we consider functions $u_h$ that are joint quasimodes of two semiclassical pseudodifferential operators $p_1(x,hD)$ and $p_2(x,hD)$ . We develop $L^p$ estimates for $u_h$ when the characteristic sets of $p_1$ and $p_2$ meet with $k$ -th order contact. This paper is the natural extension of the two-dimensional results from arXiv:1909.12559 to $n$ dimensions.

Keywords

lp estimates joint quasimodes pseudodifferential operators characteristic sets k-th order contact riemannian manifold semiclassical analysis

Cite

@article{arxiv.2504.07445,
  title  = {$L^p$ estimates for joint quasimodes of two pseudodifferential operators whose characteristic sets have $k$-th order contact},
  author = {Madelyne M. Brown and Melissa Tacy},
  journal= {arXiv preprint arXiv:2504.07445},
  year   = {2025}
}

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27pages, 2 figures

$L^p$ estimates for joint quasimodes of two pseudodifferential operators whose characteristic sets have $k$-th order contact

Abstract

Keywords

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