Abstract
A space of boundary values is constructed for the minimal symmetric operator generated by an infinite Jacobi matrix in the limit-circle case. A description of all maximal dissipative, accretive and selfadjoint extensions of such a symmetric operator is given in terms of boundary conditions at infinity. We construct a selfadjoint dilation of maximal dissipative operator and its incoming and outgoing spectral representations, which makes it possible to determine the scattering matrix of dilation. We construct a functional model of the dissipative operator and define its characteristic function. We prove a theorem on the completeness of the system of eigenvectors and associated vectors of dissipative operators.
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Allahverdiev, B.P. Extensions, Dilations and Functional Models of Infinite Jacobi Matrix. Czech Math J 55, 593–609 (2005). https://doi.org/10.1007/s10587-005-0048-3
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DOI: https://doi.org/10.1007/s10587-005-0048-3