{"paper":{"title":"On traces and modified Fredholm determinants for half-line Schr\\\"odinger operators with purely discrete spectra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Fritz Gesztesy, Klaus Kirsten","submitted_at":"2018-04-18T19:37:28Z","abstract_excerpt":"After recalling a fundamental identity relating traces and modified Fredholm determinants, we apply it to a class of half-line Schr\\\"odinger operators $(- d^2/dx^2) + q$ on $(0,\\infty)$ with purely discrete spectra. Roughly speaking, the class considered is generated by potentials $q$ that, for some fixed $C_0 > 0$, $\\varepsilon > 0$, $x_0 \\in (0, \\infty)$, diverge at infinity in the manner that $q(x) \\geq C_0 x^{(2/3) + \\varepsilon_0}$ for all $x \\geq x_0$. We treat all self-adjoint boundary conditions at the left endpoint $0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.06887","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"}