{"paper":{"title":"Some Remarks on the Spectral Problem Underlying the Camassa-Holm Hierarchy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.SP","authors_text":"Fritz Gesztesy, Rudi Weikard","submitted_at":"2013-03-22T23:08:45Z","abstract_excerpt":"We consider left-definite eigenvalue problems $A \\psi = \\lambda B \\psi$, with $A \\geq \\varepsilon I$ for some $\\varepsilon > 0$ and $B$ self-adjoint, but $B$ not necessarily positive or negative definite, applicable, in particular, to the eigenvalue problem underlying the Camassa-Holm hierarchy. In fact, we will treat a more general version where $A$ represents a positive definite Schr\\\"odinger or Sturm-Liouville operator $T$ in $L^2(\\bbR; dx)$ associated with a differential expression of the form $\\tau = - (d/dx) p(x) (d/dx) + q(x)$, $x \\in \\bbR$, and $B$ represents an operator of multiplicat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5793","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"}