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We prove Lieb--Thirring type inequalities for the discrete spectrum of $H$ in the case when $V_0\\in L^\\infty(\\br^d)$ and $V\\in L^p(\\br^d)$, $p>\\max(d/2, 1)$."},"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":"1510.03639","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-10-13T11:57:52Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"08a4df8f51cb0e8b749fa82ee68809bec43167b0bd0dc35aa376b8f60ecb5919","abstract_canon_sha256":"e13bc9b945a147530539828d8e7e518d3a2a59de7532193d04b3ad2f08665fa8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:16.593167Z","signature_b64":"dNfd0wtb7sJ2jQHBI1o0h1F3FPQSHNkpXira59/lLVmXHyQw2Peup9RT+lM3nzyB8cSk36tAUeUHboqLiwiZBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"66882c4ff17a9afb2c6023babd309aab64e38b76bfe08caf6857d93eca4eaa60","last_reissued_at":"2026-05-18T01:30:16.592475Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:16.592475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On non-selfadjoint perturbations of infinite band Schr\\\"odinger operators and Kato method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.SP","authors_text":"L. Golinskii, S. Kupin","submitted_at":"2015-10-13T11:57:52Z","abstract_excerpt":"Let $ H_0=-\\dd+V_0 $ be a multidimensional Schr\\\"odinger ope\\-rator with a real-valued potential and infinite band spectrum, and $H=H_0+V$ be its non-selfadjoint perturbation defined with the help of Kato approach. We prove Lieb--Thirring type inequalities for the discrete spectrum of $H$ in the case when $V_0\\in L^\\infty(\\br^d)$ and $V\\in L^p(\\br^d)$, $p>\\max(d/2, 1)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03639","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":"1510.03639","created_at":"2026-05-18T01:30:16.592575+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.03639v1","created_at":"2026-05-18T01:30:16.592575+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03639","created_at":"2026-05-18T01:30:16.592575+00:00"},{"alias_kind":"pith_short_12","alias_value":"M2ECYT7RPKNP","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_16","alias_value":"M2ECYT7RPKNPWLDA","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_8","alias_value":"M2ECYT7R","created_at":"2026-05-18T12:29:29.992203+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/M2ECYT7RPKNPWLDAEO5L2ME2VN","json":"https://pith.science/pith/M2ECYT7RPKNPWLDAEO5L2ME2VN.json","graph_json":"https://pith.science/api/pith-number/M2ECYT7RPKNPWLDAEO5L2ME2VN/graph.json","events_json":"https://pith.science/api/pith-number/M2ECYT7RPKNPWLDAEO5L2ME2VN/events.json","paper":"https://pith.science/paper/M2ECYT7R"},"agent_actions":{"view_html":"https://pith.science/pith/M2ECYT7RPKNPWLDAEO5L2ME2VN","download_json":"https://pith.science/pith/M2ECYT7RPKNPWLDAEO5L2ME2VN.json","view_paper":"https://pith.science/paper/M2ECYT7R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.03639&json=true","fetch_graph":"https://pith.science/api/pith-number/M2ECYT7RPKNPWLDAEO5L2ME2VN/graph.json","fetch_events":"https://pith.science/api/pith-number/M2ECYT7RPKNPWLDAEO5L2ME2VN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M2ECYT7RPKNPWLDAEO5L2ME2VN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M2ECYT7RPKNPWLDAEO5L2ME2VN/action/storage_attestation","attest_author":"https://pith.science/pith/M2ECYT7RPKNPWLDAEO5L2ME2VN/action/author_attestation","sign_citation":"https://pith.science/pith/M2ECYT7RPKNPWLDAEO5L2ME2VN/action/citation_signature","submit_replication":"https://pith.science/pith/M2ECYT7RPKNPWLDAEO5L2ME2VN/action/replication_record"}},"created_at":"2026-05-18T01:30:16.592575+00:00","updated_at":"2026-05-18T01:30:16.592575+00:00"}