Geodesic
On separation conditions for the spectral components of a~dissipative operator
Izvestiya. Mathematics , Tome 9 (1975) no. 1, pp. 113-137

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Conditions for separating the invariant subspaces corresponding to the absolutely continuous, discrete and singular spectrum of an abstract dissipative operator are obtained in terms of the characteristic function of the operator. The results are applied to ordinary differential operators with real potential and complex boundary conditions. Bibliography: 20 items. 
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B. S. Pavlov. On separation conditions for the spectral components of a~dissipative operator. Izvestiya. Mathematics , Tome 9 (1975) no. 1, pp. 113-137. http://geodesic.mathdoc.fr/item/IM2_1975_9_1_a5/