{"paper":{"title":"Wave Operators for Schr\\\"odinger Operators with Threshold Singuralities, Revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Kenji Yajima","submitted_at":"2015-08-24T10:04:49Z","abstract_excerpt":"The continuity property in the Sobolev space $W^{k,p}({\\bf R}^m)$ of wave operators of scattering theory for $m$-dimensional single-body Schr\\\"odinger operator is considered when the resolvent of the operator has singularities at the bottom of the continuous spectrum. It is shown that they are continuous in $W^{k,p}({\\bf R}^m)$, $0\\leq k \\leq 2$, for $1<p<3$ but not for $p>3$ if $m=3$ and, for $1<p<m/2$ but not for $p>m/2$ if $m\\geq 5$. This extends the previously known interval of $p$ for the continuity, $3/2<p<3$ for $m=3$ and $m/(m-2)<p<m/2$ for $m\\geq 5$. The formula which represents the i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.05738","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"}