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Vladykina","submitted_at":"2015-11-21T23:12:43Z","abstract_excerpt":"We obtain asymptotic representations as $\\lambda \\to \\infty$ in the upper and lower half-planes for the solutions of the Sturm--Liouville equation $$ -y\"+p(x)y'+q(x)y= \\lambda ^2 \\rho(x)y, \\qquad x\\in [a,b] \\subset \\mathbb{R}, $$ under the condition that $q$ is a distribution of the first-order singularity, $\\rho$ is a positive absolutely continuous function, and $p$ belongs to the space $L_2[a,b]$.\n  In supplementary part, the results are generilized on equation of the following type $$-(r^2y')'+py'+qy=\\lambda ^2 \\rho^2 y, \\qquad x\\in [a,b] \\subset \\mathbb{R},$$ where $\\lambda^2$ is the large"},"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":"1511.06934","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-11-21T23:12:43Z","cross_cats_sorted":[],"title_canon_sha256":"645b3f86a8e211b27a69387a9eabf920ed83467724ab3d4f193d5fbc23ec8ed8","abstract_canon_sha256":"4496f7cad57afb4c89308886852094a0d234fefe734584f418185b6132a2be04"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:09.899988Z","signature_b64":"ZOzPkHZC5w8NRF00H4wzqgg+x4jVRlmnWNPosCW4cWXMjBIznAmamZEDPHX9nRJDSYnS38vbXwVKFj49A/YSDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"912be964fc155dc928d556c7a6ddaf4295761eb13eb032bb815036362fda4a9e","last_reissued_at":"2026-05-18T00:44:09.899555Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:09.899555Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotics of the Solutions of the Sturm--Liouville Equation with Singular Coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"A.A. 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