{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:PKNOPLNK2NTUZVZKS3QZ6SMWBN","short_pith_number":"pith:PKNOPLNK","schema_version":"1.0","canonical_sha256":"7a9ae7adaad3674cd72a96e19f49960b6fb46170815ede6768f4006bcb6b3aad","source":{"kind":"arxiv","id":"1611.03174","version":1},"attestation_state":"computed","paper":{"title":"Spectral and pseudospectral functions of various dimensions for symmetric systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.FA","authors_text":"Vadim Mogilevskii","submitted_at":"2016-11-10T03:34:00Z","abstract_excerpt":"The main object of the paper is a symmetric system $J y'-B(t)y=\\l\\D(t) y$ defined on an interval $\\cI=[a,b) $ with the regular endpoint $a$. Let $\\f(\\cd,\\l)$ be a matrix solution of this system of an arbitrary dimension and let $(Vf)(s)=\\int\\limits_\\cI \\f^*(t,s)\\D(t)f(t)\\,dt$ be the Fourier transform of the function $f(\\cd)\\in L_\\D^2(\\cI)$. We define a pseudospectral function of the system as a matrix-valued distribution function $\\s(\\cd)$ of the dimension $n_\\s$ such that $V$ is a partial isometry from $L_\\D^2(\\cI)$ to $L^2(\\s;\\bC^{n_\\s})$ with the minimally possible kernel. Moreover, we find"},"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":"1611.03174","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-10T03:34:00Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"19243d491255a8a250ad275e5f1e285ace951a373c3c4529090db77aebec89b8","abstract_canon_sha256":"d748ef983931891e0bc4298327d8d71bebf157bd8ad71d8f556df2dd5334f4b5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:41.122151Z","signature_b64":"TDmTrqqMQW1A2G82aTDmqbNXwZBKrzzS/2WY2K4E6LeAREO5LOEHEJW+LLqBHt9zSLYrIppDDnEu7tKHyXdkAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a9ae7adaad3674cd72a96e19f49960b6fb46170815ede6768f4006bcb6b3aad","last_reissued_at":"2026-05-18T00:59:41.121521Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:41.121521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral and pseudospectral functions of various dimensions for symmetric systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.FA","authors_text":"Vadim Mogilevskii","submitted_at":"2016-11-10T03:34:00Z","abstract_excerpt":"The main object of the paper is a symmetric system $J y'-B(t)y=\\l\\D(t) y$ defined on an interval $\\cI=[a,b) $ with the regular endpoint $a$. Let $\\f(\\cd,\\l)$ be a matrix solution of this system of an arbitrary dimension and let $(Vf)(s)=\\int\\limits_\\cI \\f^*(t,s)\\D(t)f(t)\\,dt$ be the Fourier transform of the function $f(\\cd)\\in L_\\D^2(\\cI)$. We define a pseudospectral function of the system as a matrix-valued distribution function $\\s(\\cd)$ of the dimension $n_\\s$ such that $V$ is a partial isometry from $L_\\D^2(\\cI)$ to $L^2(\\s;\\bC^{n_\\s})$ with the minimally possible kernel. Moreover, we find"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03174","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":"1611.03174","created_at":"2026-05-18T00:59:41.121614+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.03174v1","created_at":"2026-05-18T00:59:41.121614+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.03174","created_at":"2026-05-18T00:59:41.121614+00:00"},{"alias_kind":"pith_short_12","alias_value":"PKNOPLNK2NTU","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_16","alias_value":"PKNOPLNK2NTUZVZK","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_8","alias_value":"PKNOPLNK","created_at":"2026-05-18T12:30:39.010887+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/PKNOPLNK2NTUZVZKS3QZ6SMWBN","json":"https://pith.science/pith/PKNOPLNK2NTUZVZKS3QZ6SMWBN.json","graph_json":"https://pith.science/api/pith-number/PKNOPLNK2NTUZVZKS3QZ6SMWBN/graph.json","events_json":"https://pith.science/api/pith-number/PKNOPLNK2NTUZVZKS3QZ6SMWBN/events.json","paper":"https://pith.science/paper/PKNOPLNK"},"agent_actions":{"view_html":"https://pith.science/pith/PKNOPLNK2NTUZVZKS3QZ6SMWBN","download_json":"https://pith.science/pith/PKNOPLNK2NTUZVZKS3QZ6SMWBN.json","view_paper":"https://pith.science/paper/PKNOPLNK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.03174&json=true","fetch_graph":"https://pith.science/api/pith-number/PKNOPLNK2NTUZVZKS3QZ6SMWBN/graph.json","fetch_events":"https://pith.science/api/pith-number/PKNOPLNK2NTUZVZKS3QZ6SMWBN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PKNOPLNK2NTUZVZKS3QZ6SMWBN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PKNOPLNK2NTUZVZKS3QZ6SMWBN/action/storage_attestation","attest_author":"https://pith.science/pith/PKNOPLNK2NTUZVZKS3QZ6SMWBN/action/author_attestation","sign_citation":"https://pith.science/pith/PKNOPLNK2NTUZVZKS3QZ6SMWBN/action/citation_signature","submit_replication":"https://pith.science/pith/PKNOPLNK2NTUZVZKS3QZ6SMWBN/action/replication_record"}},"created_at":"2026-05-18T00:59:41.121614+00:00","updated_at":"2026-05-18T00:59:41.121614+00:00"}