{"paper":{"title":"Semiclassical limits of eigenfunctions on flat $n$-dimensional tori","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Tayeb Aissiou","submitted_at":"2011-10-04T23:44:33Z","abstract_excerpt":"We provide a proof of the conjecture formulated in \\cite{Jak97,JNT01} which states that on a $n$-dimensional flat torus $\\T^{n}$, the Fourier transform of squares of the eigenfunctions $|\\phi_\\lambda|^2$ of the Laplacian have uniform $l^n$ bounds that do not depend on the eigenvalue $\\lambda$. The proof is a generalization of the argument by Jakobson, {\\it et al}. for the lower dimensional cases. These results imply uniform bounds for semiclassical limits on $\\TT^{n+2}$. We also prove a geometric lemma that bounds the number of codimension-one simplices which satisfy a certain restriction on a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.0871","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"}