Geodesic
Extensions, dilations and functional models of infinite Jacobi matrix
Czechoslovak Mathematical Journal, Tome 55 (2005) no. 3, pp. 593-609.

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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.
Classification : 47A20, 47A40, 47A45, 47B25, 47B36, 47B39, 47B44
Keywords: infinite Jacobi matrix; symmetric operator; selfadjoint and nonselfadjoint extensions; maximal dissipative operator; selfadjoint dilation; scattering matrix; functional model; characteristic function; completeness of the system of eigenvectors and associated vectors 
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     author = {Allahverdiev, B. P.},
     title = {Extensions, dilations and functional models of infinite {Jacobi} matrix},
     journal = {Czechoslovak Mathematical Journal},
     pages = {593--609},
     publisher = {mathdoc},
     volume = {55},
     number = {3},
     year = {2005},
     mrnumber = {2153085},
     zbl = {1081.47036},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2005__55_3_a2/}
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Allahverdiev, B. P. Extensions, dilations and functional models of infinite Jacobi matrix. Czechoslovak Mathematical Journal, Tome 55 (2005) no. 3, pp. 593-609. http://geodesic.mathdoc.fr/item/CMJ_2005__55_3_a2/