{"paper":{"title":"On unique continuation for Schr\\\"odinger operators of fractional and higher orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ihyeok Seo","submitted_at":"2013-01-11T11:31:34Z","abstract_excerpt":"In this note we study the property of unique continuation for solutions of $|(-\\Delta)^{\\alpha/2}u|\\leq|Vu|$, where $V$ is in a function class of potentials including $\\bigcup_{p>n/\\alpha}L^p(\\mathbb{R}^n)$ for $n-1\\leq\\alpha<n$. In particular, when $n=2$, our result gives a unique continuation theorem for the fractional ($1<\\alpha<2$) Schr\\\"odinger operator $(-\\Delta)^{\\alpha/2}+V(x)$ in the full range of $\\alpha$ values."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2460","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":""},"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"}