{"paper":{"title":"$L^p$ boundedness of wave operators for higher order schr\\\"odinger operators with threshold eigenvalues","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Kevin LaMaster, M. Burak Erdogan, William R. Green","submitted_at":"2025-06-19T14:58:07Z","abstract_excerpt":"We consider the higher order Schr\\\"odinger operator $H=(-\\Delta)^m+V(x)$ in $n$ dimensions with real-valued potential $V$ when $n>2m$, $m\\in \\mathbb N$ when $H$ has a threshold eigenvalue. We adapt our recent results for $m\\geq 1$ when $n>4m$ to lower dimensions $2m<n\\leq 4m$ to show that when $H$ has a threshold eigenvalue and no resonances, the wave operators are bounded on $L^p(\\mathbb R^n)$ for the natural range $1\\leq p<\\frac{2n}{n-1}$ when $n$ is odd and $1\\leq p<\\frac{2n}{n-2}$ when $n$ is even. We further show that if the zero energy eigenfunctions are orthogonal to $x^\\alpha V(x)$ for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.16378","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.16378/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"}