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Zapiski Nauchnykh Seminarov LOMI, 1989, Volume 178, Pages 57–91 (Mi znsl4676)  

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.
English version:
Journal of Soviet Mathematics, 1992, Volume 61, Issue 2, Pages 1981–2002
DOI: https://doi.org/10.1007/BF01095663
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
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
Citation in format AMSBIB
\Bibitem{Sol89}
\by B.~M.~Solomyak
\paper On the functional model for dissipative operators. The coordinate-free approach
\inbook Investigations on linear operators and function theory. Part~18
\serial Zap. Nauchn. Sem. LOMI
\yr 1989
\vol 178
\pages 57--91
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl4676}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1037765}
\zmath{https://zbmath.org/?q=an:0784.47018|0735.47005}
\transl
\jour J. Soviet Math.
\yr 1992
\vol 61
\issue 2
\pages 1981--2002
\crossref{https://doi.org/10.1007/BF01095663}
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  • https://www.mathnet.ru/eng/znsl/v178/p57
  • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Записки научных семинаров ПОМИ
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