{"paper":{"title":"Properties of the map associated with recovering of the Sturm-Liouville operator by its spectral function. Uniform stability in the scale of Sobolev spaces","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":"2010-10-26T09:48:49Z","abstract_excerpt":"Denote by $L_D$ the Sturm-Liouville operator $Ly=-y\" +q(x)y$ on the finite interval $[0,\\pi]$ with Dirichlet boundary conditions $y(0)=y(\\pi)=0$. Let $\\{\\lambda_k\\}_1^\\infty$ and $\\{\\alpha_k\\}_1^\\infty$ be the sequences of the eigenvalues and norming constants of this operator. For all $\\theta \\geqslant 0$ we study the map $F: W_2^{\\theta} \\to l_D^\\theta$ defined by $F(\\sigma) =\\{s_k\\}_1^\\infty$. Here $\\sigma= \\int q $ is the primitive of $q$, $\\bold s = \\{s_k\\}_1^\\infty$ be regularized spectral data defined by $s_{2k} =\\sqrt{\\lambda_k}-k,\\ s_{2k-1}=\\alpha_k-\\pi/2$ and $l_D^\\theta$ are special"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5344","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"}