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Section 1.1 contains the results of M. S. Livšic presented in various versions in the books of M. S. Livšic [L18], M. S. Brodsky [B38] and M. S. Livšic and A. A. Yantsevich [L32]. The open system introduced by M. S. Livšic in [L16] contains, per se, all characteristic properties on which the dilation theory [N11, N12] and the theory of characteristic functions [L29] are based. M. S. Livšic’s observation that the triangulation of an operator A corresponds to the factorization of its characteristic function SΔ(λ) underlies his theory of triangular models constructed in 1954.

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  • 发表日期：

    2025年

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  • Vladimir A. Zolotarev

摘要

Section 1.1 contains the results of M. S. Livšic presented in various versions in the books of M. S. Livšic [L18], M. S. Brodsky [B38] and M. S. Livšic and A. A. Yantsevich [L32]. The open system introduced by M. S. Livšic in [L16] contains, per se, all characteristic properties on which the dilation theory [N11, N12] and the theory of characteristic functions [L29] are based. M. S. Livšic’s observation that the triangulation of an operator A corresponds to the factorization of its characteristic function SΔ(λ) underlies his theory of triangular models constructed in 1954.