{"paper":{"title":"Sampling solutions of Schr\\\"odinger equations on combinatorial graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Isaac Z. Pesenson","submitted_at":"2015-02-12T13:28:08Z","abstract_excerpt":"We consider functions on a graph $G$ whose evolution in time $-\\infty<t<\\infty$ is governed by a Schr\\\"{o}dinger type equation with a combinatorial Laplace operator on the right side. For a given subset $S$ of vertices of $G$ we compute a cut-off frequency $\\omega>0$ such that solutions to a Cauchy problem with initial data in $PW_{\\omega}(G)$ are completely determined by their samples on $S\\times \\{k\\pi/\\omega\\},$ where $k\\in \\mathbf{N}$. It is shown that in the case of a bipartite graph our results are sharp."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.07688","kind":"arxiv","version":2},"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"}