Abstract
A new definition of the characteristic function is introduced for contractions on Hilbert spaces. The relationship with other definitions is established. A factorization formula corresponding to an invariant subspace is obtained. Bibliography: 3 titles.
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References
B. Sz.-Nagy and C. Foiaş,Harmonic Analysis of Operators on Hilbert Space, North-Holland, Amsterdam, and Akad. Kiadó, Budapest (1970).
N. K. Nikolskii and V. I. Vasyunin, “A unified approach to function models, and the transcription problem,” in:Operator Theory: Advances and Applications, Vol. 41, Birkhäuser, Basel-Boston (1989), pp. 405–434.
V. I. Vasyunin, “Two classical theorems on a model theory in a coordinate-free presentation,”Zap. Nauchn. Semin. LOMI,178, 5–22 (1989).
Additional information
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 247, 1997, pp. 71–78.
Translated by V. V. Kapustin.
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Kapustin, V.V. Characteristic functions and their factorizations. J Math Sci 101, 3088–3092 (2000). https://doi.org/10.1007/BF02673733
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DOI: https://doi.org/10.1007/BF02673733