{"paper":{"title":"The $L^{p}$ boundedness of the wave operators for matrix Schr\\\"{o}dinger equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Ricardo Weder","submitted_at":"2019-12-30T03:05:06Z","abstract_excerpt":"We prove that the wave operators for $n \\times n$ matrix Schr\\\"odinger equations on the half line, with general selfadjoint boundary condition, are bounded in the spaces $L^p(\\mathbb R^+, \\mathbb C^n), 1 < p < \\infty, $ for slowly decaying selfadjoint matrix potentials, $V, $ that satisfy $\\int_{0}^{\\infty }\\, (1+x) |V(x)|\\, dx < \\infty.$ Moreover, assuming that $\\int_{0}^{\\infty }\\, (1+x^\\gamma) |V(x)|\\, dx < \\infty, \\gamma > \\frac{5}{2},$ and that the scattering matrix is the identity at zero and infinite energy, we prove that the wave operators are bounded in $L^1(\\mathbb R^+, \\mathbb C^n),"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.12793","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1912.12793/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}