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 $l^2$ by the second-order difference expression
$$
(\Lambda y)_n=a_{n-1}y_{n-1}+b_ny_n+a_ny_{n+1}
$$
in the Weyl limit-circle case, where $n$ runs through the integer points on the half-line or the whole line, and the coefficients $a_n$ and $b_n$ 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.
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