{"paper":{"title":"Transformations of Nevanlinna operator-functions and their fixed points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Yu.M. Arlinski\\u{i}","submitted_at":"2017-06-03T17:01:57Z","abstract_excerpt":"We give a new characterization of the class ${\\bf N}^0_{\\mathfrak M}[-1,1]$ of the operator-valued in the Hilbert space ${\\mathfrak M}$ Nevanlinna functions that admit representations as compressed resolvents ($m$-functions) of selfadjoint contractions. We consider the automorphism ${\\bf \\Gamma}:$ $M(\\lambda){\\mapsto}M_{{\\bf \\Gamma}}(\\lambda):=\\left((\\lambda^2-1)M(\\lambda)\\right)^{-1}$ of the class ${\\bf N}^0_{\\mathfrak M}[-1,1]$ and construct a realization of $M_{{\\bf \\Gamma}}(\\lambda)$ as a compressed resolvent. The unique fixed point of ${\\bf\\Gamma}$ is the $m$-function of the block-operato"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00982","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"}