{"paper":{"title":"An inverse problem for self-adjoint positive Hankel operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Alexander Pushnitski, Patrick Gerard","submitted_at":"2014-01-09T15:58:47Z","abstract_excerpt":"For a sequence $\\{\\alpha_n\\}_{n=0}^\\infty$, we consider the Hankel operator $\\Gamma_\\alpha$, realised as the infinite matrix in $\\ell^2$ with the entries $\\alpha_{n+m}$. We consider the subclass of such Hankel operators defined by the \"double positivity\" condition $\\Gamma_\\alpha\\geq0$, $\\Gamma_{S^*\\alpha}\\geq0$; here $S^*\\alpha$ is the shifted sequence $\\{\\alpha_{n+1}\\}_{n=0}^\\infty$. We prove that in this class, the sequence $\\alpha$ is uniquely determined by the spectral shift function $\\xi_\\alpha$ for the pair $\\Gamma_\\alpha^2$, $\\Gamma_{S^*\\alpha}^2$. We also describe the class of all func"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.2042","kind":"arxiv","version":2},"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"}