{"paper":{"title":"A system coupling and Donoghue classes of Herglotz-Nevanlinna functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.FA","authors_text":"Eduard Tsekanovskii, Konstantin Makarov, Sergey Belyi","submitted_at":"2015-06-22T14:33:07Z","abstract_excerpt":"We study the impedance functions of conservative L-systems with the unbounded main operators. In addition to the generalized Donoghue class $\\sM_\\kappa$ of Herglotz-Nevanlinna functions considered by the authors earlier, we introduce \"inverse\" generalized Donoghue classes $\\sM_\\kappa^{-1}$ of functions satisfying a different normalization condition on the generating measure, with a criterion for the impedance function $V_\\Theta(z)$ of an L-system $\\Theta$ to belong to the class $\\sM_\\kappa^{-1}$ presented.\n  In addition, we establish a connection between \"geometrical\" properties of two L-syste"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06627","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"}