Extensions of symmetric infinite Jacobi operator

Abstract

A space of positive boundary values is constructed for a positive definite minimal symmetric operator generated by an infinite Jacobi matrix in limit-circle case. A description of all solvable, maximal dissipative (accumulative) solvable, self-adjoint solvable, positive definite self-adjoint and non-positive definite self-adjoint extensions of such a symmetric operator is given in terms of boundary conditions at infinity.Keywords: infinite Jacobi matrix; symmetric operator; space of positive boundary values; solvable extensions; positive definite self-adjoint and non-self-adjoint extensions; maximal dissipative operator