Geodesic
On Connection between Characterestic Functions and the Caratheodori Class Functions
Serdica Mathematical Journal, Tome 32 (2006) no. 4, pp. 289-302.

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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.
Keywords: Characterestic Function, Caratheodori Class Function, Colligation, Homographic Transformation 
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     author = {Zolotarev, Vladimir A. and Hatamleh, Ra\'ed},
     title = {On {Connection} between {Characterestic} {Functions} and the {Caratheodori} {Class} {Functions}},
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Zolotarev, Vladimir A.; Hatamleh, Raéd. On Connection between Characterestic Functions and the Caratheodori Class Functions. Serdica Mathematical Journal, Tome 32 (2006) no. 4, pp. 289-302. http://geodesic.mathdoc.fr/item/SMJ2_2006_32_4_a1/