Geodesic
On general approach to construction of self-adjoint dilation for dissipative operator
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 49, Tome 503 (2021), pp. 121-136

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On general approach to construction of self-adjoint dilation for dissipative operator. A general approach is presented to the construction of a self-adjoint dilation for a density defined dissipative operator with nonempty set of regular points. The construction involves the boundary pairs for maximal symmetric operators. Some partial cases are considered. A minimality criterion for the resulting dilation is proved. 
@article{ZNSL_2021_503_a7,
     author = {D. V. Tretyakov and Yu. L. Kudryashov},
     title = {On general approach to construction of self-adjoint dilation for dissipative operator},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {121--136},
     publisher = {mathdoc},
     volume = {503},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_503_a7/}
}
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D. V. Tretyakov; Yu. L. Kudryashov. On general approach to construction of self-adjoint dilation for dissipative operator. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 49, Tome 503 (2021), pp. 121-136. http://geodesic.mathdoc.fr/item/ZNSL_2021_503_a7/