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Potapov-Ginsburg Transformation and Functional Models of Non-Dissipative Operators

Zolotarev, Vladimir A.;  Hatamleh, Raéd — 2009

Serdica Mathematical Journal

2000 Mathematics Subject Classification: Primary 47A20, 47A45; Secondary 47A48. A relation between an arbitrary bounded operator A and dissipative operator A+, built by A in the following way A+ = A+ij*Q-j, where A-A* = ij*Jj, (J = Q+-Q- is involution), is studied. The characteristic functions of the operators A and A+ are expressed by each other using the known Potapov-Ginsburg linear-fractional transformations. The explicit form of the resolvent (A-lI)-1 is expressed by (A+-lI)-1 and...

On Connection between Characterestic Functions and the Caratheodori Class Functions

Zolotarev, Vladimir A.;  Hatamleh, Raéd — 2006

Serdica Mathematical Journal

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.

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