{"paper":{"title":"Pointwise bounds for joint eigenfunctions of quantum completely integrable systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Jeffrey Galkowski, John A. Toth","submitted_at":"2018-10-09T20:17:55Z","abstract_excerpt":"Let $(M,g)$ be a compact Riemannian manifold and $P_1:=-h^2\\Delta_g+V(x)-E_1$ so that $dp_1\\neq 0$ on $p_1=0$. We assume that $P_1$ is quantum completely integrable in the sense that there exist functionally independent pseuodifferential operators $P_2,\\dots P_n$ with $[P_i,P_j]=0$, $i,j=1,\\dots ,n$. We study the pointwise bounds for the joint eigenfunctions, $u_h$ of the system $\\{P_i\\}_{i=1}^n$ with $P_1u_h=E_1u_h+o(1)$. We first give polynomial improvements over the standard H\\\"ormander bounds for typical points in $M$. In two and three dimensions, these estimates agree with the Hardy expon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04232","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}