$L^p$ estimates for joint quasimodes of two pseudodifferential operators whose characteristic sets have $k$-th order contact
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866910908285976576 |
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| author | Brown, Madelyne M. Tacy, Melissa |
| author_facet | Brown, Madelyne M. Tacy, Melissa |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_07445 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $L^p$ estimates for joint quasimodes of two pseudodifferential operators whose characteristic sets have $k$-th order contact Brown, Madelyne M. Tacy, Melissa Analysis of PDEs 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. |
| title | $L^p$ estimates for joint quasimodes of two pseudodifferential operators whose characteristic sets have $k$-th order contact |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2504.07445 |