Geodesic
Nonunitary operators with absolutely continuous spectrum
Izvestiya. Mathematics , Tome 3 (1969) no. 1, pp. 51-63

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Sufficient conditions are found for the linear similarity of a nonunitary operator $T$ to a unitary operator with absolutely continuous spectrum. The results obtained are applied to second-order differential operators. 
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     author = {L. A. Sakhnovich},
     title = {Nonunitary operators with absolutely continuous spectrum},
     journal = {Izvestiya. Mathematics },
     pages = {51--63},
     publisher = {mathdoc},
     volume = {3},
     number = {1},
     year = {1969},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1969_3_1_a4/}
}
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L. A. Sakhnovich. Nonunitary operators with absolutely continuous spectrum. Izvestiya. Mathematics , Tome 3 (1969) no. 1, pp. 51-63. http://geodesic.mathdoc.fr/item/IM2_1969_3_1_a4/