{"paper":{"title":"Ordinary differential equations with point interactions: An inverse problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Cristina Jorge, Joao Nuno Prata, Nuno Costa Dias","submitted_at":"2018-11-02T20:47:25Z","abstract_excerpt":"Given a linear ordinary differential equation (ODE) on $\\RE$ and a set of interface conditions at a finite set of points $I \\subset \\RE$, we consider the problem of determining another differential equation whose {\\it global} solutions satisfy the original ODE on $\\RE \\backslash I $, and the interface conditions at $I $. Using an extension of the product of distributions with non-intersecting singular supports presented in [L. H\\\"ormander, The Analysis of Linear Partial Diffe\\-rential Operators I, Springer-Verlag, 1983], we determine an {\\it intrinsic} solution of this problem, i.e. a new ODE,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.01083","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"}