{"paper":{"title":"Inverse problems for Sturm--Liouville operators with potentials from Sobolev spaces. Uniform stability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"A.A.Shkalikov, A.M.Savchuk","submitted_at":"2010-10-28T11:00:04Z","abstract_excerpt":"The paper deals with two inverse problems for Sturm--Liouville operator $Ly=-y\" +q(x)y$ on the finite interval $[0,\\pi]$. The first one is the problem of recovering of a potential by two spectra. We associate with this problem the map $F:\\, W^\\theta_2\\to l_B^\\theta,\\ F(\\sigma) =\\{s_k\\}_1^\\infty$, where $W^\\theta_2 = W^\\theta_2[0,\\pi]$ are Sobolev spaces with $\\theta\\geqslant 0$, $\\sigma=\\int q$ is a primitive of the potential $q$ and $l_B^\\theta$ are special Hilbert spaces which we construct to place in the regularized spectral data $\\bold s = \\{s_k\\}_1^\\infty$. The properties of the map $F$ a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5916","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"}