ON THE SPECTRAL THEORY OF DISSIPATIVE DIFFERENCE OPERATORS OF SECOND ORDER

Abstract

The boundary conditions at infinity are used in a description of all maximal dissipative extensions of the minimal symmetric operator generated in the Hilbert space by the second-order difference expression in the Weyl limit-circle case, where runs through the integer points on the half-line or the whole line, and the coefficients and are real. The characteristic functions of the dissipative extensions are computed. Completeness theorems are obtained for the system of eigenvectors and associated vectors.Bibliography: 13 titles.