On Connection between Characterestic Functions and the Caratheodori Class Functions

2000 Mathematics Subject Classification: 47A65, 45S78.

Connection of characteristic functions S(z) of nonunitary operator T with the functions of Caratheodori class is established. It was demonstrated that the representing measures from integral representation of the function of Caratheodori's class are defined by restrictions of spectral measures of unitary dilation, of a restricted operator T on the corresponding defect subspaces.