Geodesic
Characteristic functions and their factorizations
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 25, Tome 247 (1997), pp. 71-78

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A new definition of the characteristic function is introduced for contractions on Hilbert spaces. The relationship with the other definitions is established. A factorization formula corresponding to an invariant subspace is obtained. 
@article{ZNSL_1997_247_a4,
     author = {V. V. Kapustin},
     title = {Characteristic functions and their factorizations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {71--78},
     publisher = {mathdoc},
     volume = {247},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_247_a4/}
}
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V. V. Kapustin. Characteristic functions and their factorizations. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 25, Tome 247 (1997), pp. 71-78. http://geodesic.mathdoc.fr/item/ZNSL_1997_247_a4/