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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. 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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. 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