Geodesic
Isomorphism of two functional models of operators of the class~$C_0$
Matematičeskie zametki, Tome 23 (1978) no. 6, pp. 863-872.

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A theorem is proved, from which follows an explicit expression for an operator, transforming the well-known Nagy-Foias functional model for a contraction of the class $C_0$ into a Livshitz–Polyatskii type model. 
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     author = {L. B. Golinskii},
     title = {Isomorphism of two functional models of operators of the class~$C_0$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {863--872},
     publisher = {mathdoc},
     volume = {23},
     number = {6},
     year = {1978},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1978_23_6_a8/}
}
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L. B. Golinskii. Isomorphism of two functional models of operators of the class~$C_0$. Matematičeskie zametki, Tome 23 (1978) no. 6, pp. 863-872. http://geodesic.mathdoc.fr/item/MZM_1978_23_6_a8/