Geodesic
Potapov-Ginsburg Transformation and Functional Models of Non-Dissipative Operators
Serdica Mathematical Journal, Tome 35 (2009) no. 4, pp. 343-358.

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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 (A+*-lI)-1 in terms of these transformations. Furthermore, the functional model [10, 12] of non-dissipative operator A in terms of a model for A+, which evolves the results, was obtained by Naboko, S. N. [7]. The main constructive elements of the present construction are shown to be the elements of the Potapov-Ginsburg transformation for corresponding characteristic functions. A relation between an arbitrary bounded operator A and dissipative operator A+, built by A in the following way A+ = A + iϕ
Keywords: Colligations, Non-Dissipative Operator, Functional Model, Resolvent Operator 
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     title = {Potapov-Ginsburg {Transformation} and {Functional} {Models} of {Non-Dissipative} {Operators}},
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Zolotarev, Vladimir A.; Hatamleh, Raéd. Potapov-Ginsburg Transformation and Functional Models of Non-Dissipative Operators. Serdica Mathematical Journal, Tome 35 (2009) no. 4, pp. 343-358. http://geodesic.mathdoc.fr/item/SMJ2_2009_35_4_a1/