{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:QQQ6ZAHOCWU7DCSQ2ZGVAFELDW","short_pith_number":"pith:QQQ6ZAHO","schema_version":"1.0","canonical_sha256":"8421ec80ee15a9f18a50d64d50148b1db7a02d04e35eba693233a1ca933dc454","source":{"kind":"arxiv","id":"1107.2552","version":4},"attestation_state":"computed","paper":{"title":"Asymptotic Analysis of Non-self-adjoint Hill Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"O. A. Veliev","submitted_at":"2011-07-13T13:46:11Z","abstract_excerpt":"We obtain the uniform asymptotic formulas for the eigenvalues and eigenfunctions of the Sturm-Liouville operators L_{t}(q) with a potential q\\inL_{1}[0,1] and with t-periodic boundary conditions, t\\in(-{\\pi},{\\pi}]. Using these formulas, we find sufficient conditions on the potential q such that the number of spectral singularities in the spectrum of the Hill operator L(q) in L_{2}(-\\infty,\\infty) is finite. Then we prove that the operator L(q) has no spectral singularities at infinity and it is an asymptotically spectral operator provided that the potential q satisfies the sufficient conditio"},"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":"1107.2552","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-07-13T13:46:11Z","cross_cats_sorted":[],"title_canon_sha256":"4bf345aec78e7c546e51bc4d1f9797d7bb289f4875ffda54eaad61f2958a5f78","abstract_canon_sha256":"6e2f045b66226a722b1a5d81613f965904e45b0287d750f28f800ae98525bf5e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:50:25.833940Z","signature_b64":"PkczwoBDxlCupdmbKEiu7c/V2LWzjl8tNNjNpiTWijfd5dGNocmd7uhBz2pT7Kwq0YMl1e//NAUaEtHs/qM9Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8421ec80ee15a9f18a50d64d50148b1db7a02d04e35eba693233a1ca933dc454","last_reissued_at":"2026-05-18T03:50:25.833064Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:50:25.833064Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic Analysis of Non-self-adjoint Hill Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"O. A. Veliev","submitted_at":"2011-07-13T13:46:11Z","abstract_excerpt":"We obtain the uniform asymptotic formulas for the eigenvalues and eigenfunctions of the Sturm-Liouville operators L_{t}(q) with a potential q\\inL_{1}[0,1] and with t-periodic boundary conditions, t\\in(-{\\pi},{\\pi}]. Using these formulas, we find sufficient conditions on the potential q such that the number of spectral singularities in the spectrum of the Hill operator L(q) in L_{2}(-\\infty,\\infty) is finite. Then we prove that the operator L(q) has no spectral singularities at infinity and it is an asymptotically spectral operator provided that the potential q satisfies the sufficient conditio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2552","kind":"arxiv","version":4},"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":"1107.2552","created_at":"2026-05-18T03:50:25.833202+00:00"},{"alias_kind":"arxiv_version","alias_value":"1107.2552v4","created_at":"2026-05-18T03:50:25.833202+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.2552","created_at":"2026-05-18T03:50:25.833202+00:00"},{"alias_kind":"pith_short_12","alias_value":"QQQ6ZAHOCWU7","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_16","alias_value":"QQQ6ZAHOCWU7DCSQ","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_8","alias_value":"QQQ6ZAHO","created_at":"2026-05-18T12:26:39.201973+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/QQQ6ZAHOCWU7DCSQ2ZGVAFELDW","json":"https://pith.science/pith/QQQ6ZAHOCWU7DCSQ2ZGVAFELDW.json","graph_json":"https://pith.science/api/pith-number/QQQ6ZAHOCWU7DCSQ2ZGVAFELDW/graph.json","events_json":"https://pith.science/api/pith-number/QQQ6ZAHOCWU7DCSQ2ZGVAFELDW/events.json","paper":"https://pith.science/paper/QQQ6ZAHO"},"agent_actions":{"view_html":"https://pith.science/pith/QQQ6ZAHOCWU7DCSQ2ZGVAFELDW","download_json":"https://pith.science/pith/QQQ6ZAHOCWU7DCSQ2ZGVAFELDW.json","view_paper":"https://pith.science/paper/QQQ6ZAHO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1107.2552&json=true","fetch_graph":"https://pith.science/api/pith-number/QQQ6ZAHOCWU7DCSQ2ZGVAFELDW/graph.json","fetch_events":"https://pith.science/api/pith-number/QQQ6ZAHOCWU7DCSQ2ZGVAFELDW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QQQ6ZAHOCWU7DCSQ2ZGVAFELDW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QQQ6ZAHOCWU7DCSQ2ZGVAFELDW/action/storage_attestation","attest_author":"https://pith.science/pith/QQQ6ZAHOCWU7DCSQ2ZGVAFELDW/action/author_attestation","sign_citation":"https://pith.science/pith/QQQ6ZAHOCWU7DCSQ2ZGVAFELDW/action/citation_signature","submit_replication":"https://pith.science/pith/QQQ6ZAHOCWU7DCSQ2ZGVAFELDW/action/replication_record"}},"created_at":"2026-05-18T03:50:25.833202+00:00","updated_at":"2026-05-18T03:50:25.833202+00:00"}