{"paper":{"title":"On the Weyl-Titchmarsh and Liv\\v{s}ic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Eduard Tsekanovskii, Konstantin Makarov","submitted_at":"2013-01-19T23:32:47Z","abstract_excerpt":"We establish a mutual relationship between main analytic objects for the dissipative extension theory of a symmetric operator $\\dot A$ with deficiency indices $(1,1)$. In particular, we introduce the Weyl-Titchmarsh function $\\cM$ of a maximal dissipative extension $\\hat A$ of the symmetric operator $\\dot A$. Given a reference self-adjoint extension $A$ of $\\dot A$, we introduce a von Neumann parameter $\\kappa$, $|\\kappa|<1$, characterizing the domain of the dissipative extension $\\hat A$ against $\\Dom (A)$ and show that the pair $(\\kappa, \\cM)$ is a complete unitary invariant of the triple $("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4610","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"}