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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1410.2964","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-10-11T07:32:37Z","cross_cats_sorted":[],"title_canon_sha256":"643a2c46341bd854047dc7d5502037b6f075c05ff640d5e6b088b3996c84533e","abstract_canon_sha256":"8481d550466871ae694488308fe907ec4766e8fd0dec9e64977fd2e8132d007d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:17.372443Z","signature_b64":"di9xaMX94+I7crjKcbbrck+FyJreDd1I7puSz/T1c1i76tWTuBY/f7cM+66de3EkL6yRUQ4UZ2aFO8xsjyTTDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47e4069263c3f05de556488ae6c75ae5b2eae096ba7101ccdb0235f88db2d68c","last_reissued_at":"2026-05-18T02:40:17.372008Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:17.372008Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1410.2964","created_at":"2026-05-18T02:40:17.372071+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.2964v1","created_at":"2026-05-18T02:40:17.372071+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.2964","created_at":"2026-05-18T02:40:17.372071+00:00"},{"alias_kind":"pith_short_12","alias_value":"I7SANETDYPYF","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_16","alias_value":"I7SANETDYPYF3ZKW","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_8","alias_value":"I7SANETD","created_at":"2026-05-18T12:28:33.132498+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/I7SANETDYPYF3ZKWJCFONR224W","json":"https://pith.science/pith/I7SANETDYPYF3ZKWJCFONR224W.json","graph_json":"https://pith.science/api/pith-number/I7SANETDYPYF3ZKWJCFONR224W/graph.json","events_json":"https://pith.science/api/pith-number/I7SANETDYPYF3ZKWJCFONR224W/events.json","paper":"https://pith.science/paper/I7SANETD"},"agent_actions":{"view_html":"https://pith.science/pith/I7SANETDYPYF3ZKWJCFONR224W","download_json":"https://pith.science/pith/I7SANETDYPYF3ZKWJCFONR224W.json","view_paper":"https://pith.science/paper/I7SANETD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.2964&json=true","fetch_graph":"https://pith.science/api/pith-number/I7SANETDYPYF3ZKWJCFONR224W/graph.json","fetch_events":"https://pith.science/api/pith-number/I7SANETDYPYF3ZKWJCFONR224W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I7SANETDYPYF3ZKWJCFONR224W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I7SANETDYPYF3ZKWJCFONR224W/action/storage_attestation","attest_author":"https://pith.science/pith/I7SANETDYPYF3ZKWJCFONR224W/action/author_attestation","sign_citation":"https://pith.science/pith/I7SANETDYPYF3ZKWJCFONR224W/action/citation_signature","submit_replication":"https://pith.science/pith/I7SANETDYPYF3ZKWJCFONR224W/action/replication_record"}},"created_at":"2026-05-18T02:40:17.372071+00:00","updated_at":"2026-05-18T02:40:17.372071+00:00"}