{"paper":{"title":"Weighted local Weyl laws for elliptic operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Alejandro Rivera (IF)","submitted_at":"2018-01-22T08:55:25Z","abstract_excerpt":"Let $A$ be an elliptic pseudo-differential operator of order $m$ on a closed manifold $\\mathcal{X}$ of dimension $n>0$, formally positive self-adjoint with respect to some positive smooth density $d\\mu_\\mathcal{X}$. Then, the spectrum of $A$ is made up of a sequence of eigenvalues $(\\lambda_k)_{k\\geq 1}$ whose corresponding eigenfunctions $(e_k)_{k\\geq 1}$ are $C^\\infty$ smooth. Fix $s\\in\\mathbb{R}$ and define \\[ K_L^s(x,y)=\\sum_{0<\\lambda_k\\leq L}\\lambda_k^{-s} e_k(x)\\overline{e_k(y)}\\, .\\] We derive asymptotic formulae near the diagonal for the kernels $K_L^s(x,y)$ when $L\\rightarrow +\\infty"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.07598","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"}