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Zapiski Nauchnykh Seminarov LOMI, 1989, Volume 178, Pages 57–91
(Mi znsl4676)
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This article is cited in 9 scientific papers (total in 9 papers)
On the functional model for dissipative operators. The coordinate-free approach
B. M. Solomyak
Abstract:
The paper is based on seminar talks and is mostly instructional. Dissipative operators are studied by means of their Caley transforms using the coordinate-free model for contractions developed by N. K. Nikolskii and V. I. Vasyunin. It is shown that different known froms of the characteristic functions and self-adjoint dilation can be derived from a general scheme. Also we find new formulae for the dilation and its eigen-functions which generalise those obtained by B. S. Pavlov for the Shrödinger operator on a half-line with a real-valued potential and a nonreal boundary condition. Several examples are considered.
Citation:
B. M. Solomyak, “On the functional model for dissipative operators. The coordinate-free approach”, Investigations on linear operators and function theory. Part 18, Zap. Nauchn. Sem. LOMI, 178, "Nauka", Leningrad. Otdel., Leningrad, 1989, 57–91; J. Soviet Math., 61:2 (1992), 1981–2002
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https://www.mathnet.ru/eng/znsl4676 https://www.mathnet.ru/eng/znsl/v178/p57
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Abstract page: | 154 | Full-text PDF : | 68 |
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