{"paper":{"title":"Desirable Decompositions of Generalized Nevanlinna Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Muhamed Borogovac","submitted_at":"2014-12-31T21:41:05Z","abstract_excerpt":"For a given generalized Nevanlinna function $Q\\in N_{\\kappa }\\left( H \\right)$, we study decompositions that satisfy: $Q=Q_{1}+Q_{2}$; $Q_{i}{\\in N}_{\\kappa_{i}}\\left( H \\right)$, and $\\kappa_{1}+\\kappa_{2}=\\kappa $, $0\\le \\kappa_{i}$, which we call desirable decompositions. In this paper, some sufficient conditions for such decompositions of $Q$ are given.\n  One of the main results is a new operator representation of $\\hat{Q}\\left(z\\right):=-{Q(z)}^{-1}$ if $Q\\left( z \\right):=\\Gamma_{0}^{+}\\left( A-z\\right)^{-1}\\Gamma_{0}$, where $A$ is a bounded self-adjoint operator in a Pontryagin space. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00214","kind":"arxiv","version":3},"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"}