Functional model for dissipative operators. A coordinate-free approach

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The paper has, basically, a methodical character. Dissipative operators are investigated with the aid of the Cayley contraction-transformation on the basis of the "coordinate-free model" of V. L Vasyunin and N. K. Nikol'skii. It is shown that the known forms of the characteristic function and of the selfadjoint dilation can be obtained as various realization of a general scheme. One obtains also new formulas for the dilation and its eigenfunctions, generalizing B. S. Pavlov's formulas for the Schrödinger operator on the semiaxis with a real potential and complex boundary condition. Examples are considered.

Original languageEnglish
Pages (from-to)1981-2002
Number of pages22
JournalJournal of Soviet Mathematics
Issue number2
StatePublished - Aug 1992


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