{"paper":{"title":"Graph Laplacians do not generate strongly continuous semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Christoph Schumacher, Thomas Kalmes","submitted_at":"2015-08-24T13:15:29Z","abstract_excerpt":"We show that for graph Laplacians $\\Delta_G$ on a connected locally finite simplicial undirected graph $G$ with countable infinite vertex set $V$ none of the operators $\\alpha\\,\\mathrm{Id}+\\beta\\Delta_G, \\alpha,\\beta\\in\\mathbb{K},\\beta \\ne 0$, generate a strongly continuous semigroup on $\\mathbb{K}^V$ when the latter is equipped with the product topology."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.05794","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"}