Geodesic
On the functional model for dissipative operators. The coordinate-free approach
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 18, Tome 178 (1989), pp. 57-91
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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. 
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     author = {B. M. Solomyak},
     title = {On the functional model for dissipative operators. {The} coordinate-free approach},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {57--91},
     year = {1989},
     volume = {178},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1989_178_a2/}
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B. M. Solomyak. On the functional model for dissipative operators. The coordinate-free approach. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 18, Tome 178 (1989), pp. 57-91. http://geodesic.mathdoc.fr/item/ZNSL_1989_178_a2/