{"paper":{"title":"Global transformations preserving spectral data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Evgeny L. Korotyaev, Hiroshi Isozaki","submitted_at":"2013-07-07T21:51:21Z","abstract_excerpt":"We show the existence of a real analytic isomorphism between a space of impedance function $\\rho$ of the Sturm-Liouville problem\n  $- \\rho^{-2}(\\rho^2f')' + uf$ on $(0,1)$, where $u$ is a function of $\\rho, \\rho', \\rho''$, and that of potential $p$ of the Schr{\\\"o}dinger equation $- y'' + py$ on $(0,1)$, keeping their boundary conditions and spectral data.\n  This mapping is associated with the classical Liouville transformation $f \\to \\rho f$, and yields a global isomorphism between solutions to inverse problems for the Sturm-Liouville equations of the impedance form and those to the Schr{\\\"o}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1924","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"}