{"paper":{"title":"Inverse Spectral Theory for Sturm-Liouville Operators with Distributional Potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Fritz Gesztesy, Gerald Teschl, Jonathan Eckhardt, Roger Nichols","submitted_at":"2012-10-29T11:47:58Z","abstract_excerpt":"We discuss inverse spectral theory for singular differential operators on arbitrary intervals $(a,b) \\subseteq \\mathbb{R}$ associated with rather general differential expressions of the type \\[\\tau f = \\frac{1}{r} \\left(- \\big(p[f' + s f]\\big)' + s p[f' + s f] + qf\\right), \\] where the coefficients $p$, $q$, $r$, $s$ are Lebesgue measurable on $(a,b)$ with $p^{-1}$, $q$, $r$, $s \\in L^1_{\\text{loc}}((a,b); dx)$ and real-valued with $p\\not=0$ and $r>0$ a.e.\\ on $(a,b)$. In particular, we explicitly permit certain distributional potential coefficients.\n  The inverse spectral theory results deriv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.7628","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"}