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Zapiski Nauchnykh Seminarov POMI, 2021, Volume 503, Pages 121–136 (Mi znsl7104)  
On general approach to construction of self-adjoint dilation for dissipative operator

D. V. Tretyakov, Yu. L. Kudryashov

Crimea Federal University, Simferopol
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Abstract: 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.
Key words and phrases: self-adjoint dilation, dissipative operator, spaces of boundary values of the operator, maximal symmetric operator, defect operators, defect subspaces, defect index.
Received: 01.04.2021
Document Type: Article
UDC: 517.432
Language: Russian
Citation: D. V. Tretyakov, Yu. L. Kudryashov, “On general approach to construction of self-adjoint dilation for dissipative operator”, Investigations on linear operators and function theory. Part 49, Zap. Nauchn. Sem. POMI, 503, POMI, St. Petersburg, 2021, 121–136
Citation in format AMSBIB
\Bibitem{TreKud21}
\by D.~V.~Tretyakov, Yu.~L.~Kudryashov
\paper On general approach to construction of self-adjoint dilation for dissipative operator
\inbook Investigations on linear operators and function theory. Part~49
\serial Zap. Nauchn. Sem. POMI
\yr 2021
\vol 503
\pages 121--136
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl7104}
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  • https://www.mathnet.ru/eng/znsl/v503/p121
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