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It is assumed that the deficiency indices $n_\\pm(\\Tmi)$ of the corresponding minimal relation $\\Tmi$ in $\\LI$ satisfy $n_-(\\Tmi)\\leq n_+(\\Tmi)$. We describe all generalized resolvents $y=R(\\l)f, \\; f\\in\\LI,$ of $\\Tmi$ in terms of boundary problems with $\\l$-depending boundary conditions imposed on regular and singular boundary values of a function $y$ at the endpoints $a$ and $b$ respectively. We also parametriz"},"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":"1403.3955","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-03-16T19:58:01Z","cross_cats_sorted":[],"title_canon_sha256":"d6d262745cec66567ed8e16b8116454298822de4355d7c53deeaa00258066d91","abstract_canon_sha256":"b1451673b283f329f2011c774d135992c019bd7b62b622c299e2f040d07fcf94"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:13.078261Z","signature_b64":"Rlluh9lNH2wILYSpRnY7cbXwjv9z4huBn+bgyE0h+IEZ55Ff8Bsal4TKcrFzGPL885hBAxbU4lmtYRMN26T7Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68b66f35d77836d68d4adc32bd488c1da037d814b6bde507f5250415f9fa9944","last_reissued_at":"2026-05-18T02:56:13.077673Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:13.077673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On generalized resolvents and characteristic matrices of first-order symmetric systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Vadim Mogilevskii","submitted_at":"2014-03-16T19:58:01Z","abstract_excerpt":"We study general (not necessarily Hamiltonian) first-order symmetric system $J y'-B(t)y=\\D(t) f(t)$ on an interval $\\cI=[a,b) $ with the regular endpoint $a$ and singular endpoint $b$. It is assumed that the deficiency indices $n_\\pm(\\Tmi)$ of the corresponding minimal relation $\\Tmi$ in $\\LI$ satisfy $n_-(\\Tmi)\\leq n_+(\\Tmi)$. We describe all generalized resolvents $y=R(\\l)f, \\; f\\in\\LI,$ of $\\Tmi$ in terms of boundary problems with $\\l$-depending boundary conditions imposed on regular and singular boundary values of a function $y$ at the endpoints $a$ and $b$ respectively. 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