{"paper":{"title":"Perturbations of Donoghue classes and inverse problems for L-systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Eduard Tsekanovskii, Sergey Belyi","submitted_at":"2018-06-17T02:55:16Z","abstract_excerpt":"We study linear perturbations of Donoghue classes of scalar Herglotz-Nevanlinna functions by a real parameter $Q$ and their representations as impedance of conservative L-systems. Perturbation classes $\\mathfrak M^Q$, $\\mathfrak M^Q_\\kappa$, $\\mathfrak M^{-1,Q}_\\kappa$ are introduced and for each class the realization theorem is stated and proved. We use a new approach that leads to explicit new formulas describing the von Neumann parameter of the main operator of a realizing L-system and the unimodular one corresponding to a self-adjoint extension of the symmetric part of the main operator. T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06329","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"}