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

Madelyne M. Brown; Melissa Tacy

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arXiv · 2504.07445

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

Madelyne M. Brown·Melissa Tacy

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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.

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Madelyne M. Brown, Melissa Tacy. 2025-04-10. $L^p$ estimates for joint quasimodes of two pseudodifferential operators whose characteristic sets have $k$-th order contact. https://arxiv.org/abs/2504.07445

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