Abstract
We construct a function model for an operator in a Hilbert space close to an isometry. The model operator acts on the space of functions meromorphic inside and outside the unit disk. The functions from the space may be regarded as generalizations of Cauchy integrals of distributions, which gives a base for spectral analysis. We prove a theorem on the existence of such a model for one-dimensional perturbations of a unitary operator. Bibliography: 2 titles.
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REFERENCES
V. V. Kapustin, “One-dimensional perturbations of singular unitary operators,” Zap.Nauchn.Semin.POMI, 232, 118–122 (1996).
N. K. Nikolskii and V. I. Vasyunin, “A unified approach to the function models, and the transcription problem,” in: The Gohberg Anniversary Collection, Vol. 2 (Calgary, 1988), Operator Theory: Adv.Appl.,41, Birkhäuser, Basel-Boston (1989), pp. 405–434.
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Kapustin, V.V. Operators Close to Unitary Ones and Their Function Models. I. Journal of Mathematical Sciences 107, 4022–4028 (2001). https://doi.org/10.1023/A:1012484515718
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DOI: https://doi.org/10.1023/A:1012484515718