Geodesic
Dissipative Schr\"odinger operator without a
Sbornik. Mathematics, Tome 195 (2004) no. 6, pp. 897-915

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The spectral structure of a dissipative Schrödinger operator on a half-axis with complex potential having a finite first moment is analysed by the methods of scattering theory. Under the assumption of the absence of spectral singularities the absolute continuity (in the sense of a functional model) of the continuous component of the spectrum is established, the existence of bounded wave operators is proved, and the spectral representation of operators in the class under consideration is constructed with their help. 
@article{SM_2004_195_6_a6,
     author = {S. A. Stepin},
     title = {Dissipative {Schr\"odinger} operator without a},
     journal = {Sbornik. Mathematics},
     pages = {897--915},
     publisher = {mathdoc},
     volume = {195},
     number = {6},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2004_195_6_a6/}
}
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S. A. Stepin. Dissipative Schr\"odinger operator without a. Sbornik. Mathematics, Tome 195 (2004) no. 6, pp. 897-915. http://geodesic.mathdoc.fr/item/SM_2004_195_6_a6/