{"paper":{"title":"Unitary equivalence of proper extensions of a symmetric operator and the Weyl function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mark Malamud, Seppo Hassi, Vadim Mogilevskii","submitted_at":"2012-08-06T16:18:47Z","abstract_excerpt":"Let $A$ be a densely defined simple symmetric operator in $\\gH$, let $\\Pi=\\bt$ be a boundary triplet for $A^*$ and let $M(\\cd)$ be the corresponding Weyl function. It is known that the Weyl function $M(\\cd)$ determines the boundary triplet $\\Pi$, in particular, the pair ${A,A_0}$, where $A_0:= A^*\\lceil\\ker\\G_0 (= A^*_0)$, uniquely up to unitary similarity. At the same time the Weyl function corresponding to a boundary triplet for a dual pair of operators defines it uniquely only up to weak similarity.\n  In this paper we consider symmetric dual pairs ${A,A}$ generated by $A\\subset A^*$ and spe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1201","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"}