{"paper":{"title":"Weyl-Titchmarsh 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":"2012-08-23T06:21:15Z","abstract_excerpt":"We systematically develop Weyl-Titchmarsh theory for singular differential operators on arbitrary intervals $(a,b) \\subseteq \\mathbb{R}$ associated with rather general differential expressions of the type \\[\n  \\tau f = \\frac{1}{r} (- \\big(p[f' + s f]\\big)' + s p[f' + s f] + qf),] where the coefficients $p$, $q$, $r$, $s$ are real-valued and Lebesgue measurable on $(a,b)$, with $p\\neq 0$, $r>0$ a.e.\\ on $(a,b)$, and $p^{-1}$, $q$, $r$, $s \\in L^1_{\\text{loc}}((a,b); dx)$, and $f$ is supposed to satisfy [f \\in AC_{\\text{loc}}((a,b)), \\; p[f' + s f] \\in AC_{\\text{loc}}((a,b)).] In particular, thi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.4677","kind":"arxiv","version":3},"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"}