Extensions, dilations and functional models of infinite Jacobi matrix

Title:

Extensions, dilations and functional models of infinite Jacobi matrix

Creator:

Allahverdiev, B. P.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:cfebe9ed-ba92-4486-8764-6343d048f5f5
uuid:cfebe9ed-ba92-4486-8764-6343d048f5f5

Subject:

infinite Jacobi matrix, symmetric operator, selfadjoint and nonselfadjoint extensions, maximal dissipative operator, selfadjoint dilation, scattering matrix, functional model, characteristic function, and completeness of the system of eigenvectors and associated vectors

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

593-609

Source:

Czechoslovak Mathematical Journal | 2005 Volume:55 | Number:3

Harvested from:

CDK

Metadata only:

false