{"paper":{"title":"L_1-Estimates for Eigenfunctions of the Dirichlet Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Juergen Voigt, Michiel van den Berg, Rainer Hempel","submitted_at":"2013-08-22T08:33:01Z","abstract_excerpt":"For $d \\in \\N$ and $\\Omega \\ne \\emptyset$ an open set in $\\R^d$, we consider the eigenfunctions $\\Phi$ of the Dirichlet Laplacian $-\\Delta_\\Omega$ of $\\Omega$. If $\\Phi$ is associated with an eigenvalue below the essential spectrum of $-\\Delta_\\Omega$ we provide estimates for the $L_1$-norm of $\\Phi$ in terms of its $L_2$-norm and spectral data. These $L_1$-estimates are then used in the comparison of the heat content of $\\Omega$ at time $t>0$ and the heat trace at times $t' > 0$, where a two-sided estimate is established. We furthermore show that all eigenfunctions of $-\\Delta_\\Omega$ which a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4788","kind":"arxiv","version":3},"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"}