{"paper":{"title":"Dispersive estimates for fractional order Schr\\\"odinger operators","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"M. Burak Erdogan, Michael Goldberg, William Green","submitted_at":"2025-09-22T16:41:11Z","abstract_excerpt":"We prove dispersive bounds for fractional Schr\\\"odinger operators on $\\mathbb R^n$ of the form $H=(-\\Delta)^{\\alpha}+V$ with $V$ a real-valued, decaying potential and $\\alpha \\notin\\mathbb N$. We derive pointwise bounds on the resolvent operators for all $0<\\alpha<\\frac{n}{2}$, a quantitative limiting absorption principle for $\\frac12<\\alpha<\\frac{n}{2}$, and establish global dispersive estimates in dimension $n\\geq 2$ for the range $\\frac{n+1}{4}\\leq \\alpha <\\frac{n}2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.18002","kind":"arxiv","version":2},"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/2509.18002/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"}