{"paper":{"title":"Inverse resonance scattering for on rotationally symmetric manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SP","authors_text":"Evgeny Korotyaev, Hiroshi Isozaki","submitted_at":"2019-04-18T17:37:54Z","abstract_excerpt":"We discuss inverse resonance scattering for the Laplacian on a rotationally symmetric manifold $M = (0,\\infty) \\times Y$ whose rotation radius is constant outside some compact interval. The Laplacian on $M$ is unitarily equivalent to a direct sum of one-dimensional Schr\\\"odinger operators with compactly supported potentials on the half-line. We prove\n  o Asymptotics of counting function of resonances at large radius\n  o Inverse problem: The rotation radius is uniquely determined by its eigenvalues and resonances. Moreover, there exists an algorithm to recover the rotation radius from its eigen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.08908","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"}