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

2025/04/10 by Brown, Madelyne M., Tacy, Melissa
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.07445

Abstract

On a smooth, compact, n-dimensional Riemannian manifold, we consider functions u_h that are joint quasimodes of two semiclassical pseudodifferential operators p₁(x,hD) and p₂(x,hD). We develop L^p estimates for u_h when the characteristic sets of p₁ and p₂ 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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