{"paper":{"title":"A criterion for essential self-adjointness of a symmetric operator defined by some infinite hermitian matrix with unbounded entries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Tomasz Komorowski","submitted_at":"2014-10-11T07:32:37Z","abstract_excerpt":"We shall consider a double infinite, hermitian, complex entry matrix $A=[a_{x,y}]_{x,y\\in\\mathbb Z}$, with $a_{x,y}^*=a_{y,x}$, $x,y\\in\\mathbb Z$. Assuming that the matrix is almost of a finite bandwidth, i.e. there exists an integer $n> 0$ and exponent $\\gamma\\in[0,1)$ such that $ a_{x,x+z}=0$ for all $z>n\\langle x\\rangle^{\\gamma}$ and the growth of the $\\ell_1$ norm of a row is slower than $|x|^{1-\\gamma}$ for $|x|\\gg1$, i.e. $\\lim_{|x|\\to+\\infty}| x|^{\\gamma-1}\\sum_{y}|a_{xy}|=0$ we prove that the corresponding symmetric operator, defined on compactly supported sequences, is essentially sel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2964","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"}