Displaying similar documents to “On the solution of Nevanlinna Pick problem with selfadjoint extensions of symmetric linear relations in Hilbert space.”

Extensions of symmetric operators I: The inner characteristic function case

R.T.W. Martin (2015)

Concrete Operators

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Given a symmetric linear transformation on a Hilbert space, a natural problem to consider is the characterization of its set of symmetric extensions. This problem is equivalent to the study of the partial isometric extensions of a fixed partial isometry. We provide a new function theoretic characterization of the set of all self-adjoint extensions of any symmetric linear transformation B with finite equal indices and inner Livšic characteristic function θB by constructing a bijection...

Extensions, dilations and functional models of infinite Jacobi matrix

B. P. Allahverdiev (2005)

Czechoslovak Mathematical Journal

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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...