{"paper":{"title":"Compactness of iso-resonant potentials for Schr\\\"odinger operators in dimensions one and three","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Peter D. Hislop, Robert Wolf","submitted_at":"2018-03-06T13:47:43Z","abstract_excerpt":"We prove compactness of a restricted set of real-valued, compactly supported potentials $V$ for which the corresponding Schr\\\"odinger operators $H_V$ have the same resonances, including multiplicities. More specifically, let $B_R(0)$ be the ball of radius $R > 0$ about the origin in $R^d$, for $d=1,3$. Let $\\mathcal{I}_R (V_0)$ be the set of real-valued potentials in $C_0^\\infty( \\overline{B}_R(0); R)$ so that the corresponding Schr\\\"odinger operators have the same resonances, including multiplicities, as $H_{V_0}$. We prove that the set $\\mathcal{I}_R (V_0)$ is a compact subset of $C_0^\\infty"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.02172","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"}