ON DILATION THEORY AND SPECTRAL ANALYSIS OF DISSIPATIVE SCHRÖDINGER OPERATORS IN WEYL'S LIMIT-CIRCLE CASE

Abstract

Dissipative Schrodinger operators are studied in Weyl's limit-circle case. A selfadjoint dilation and a spectral model of these operators are constructed and the characteristic function is computed. Theorems on the completeness of the eigenfunctions of the dissipative operators are proved.