Geodesic
Selfadjoint dilatation of the dissipative Shrödinger operator and its resolution in terms of eigenfunctions
Sbornik. Mathematics, Tome 31 (1977) no. 4, pp. 457-478 Cet article a éte moissonné depuis la source Math-Net.Ru

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The object of the present work is the imbedding of the spectral theory for the dissipative Schrödinger operator $L$ with absolutely continuous spectrum acting in the Hilbert space $H=L_2(R^3)$ in the spectral theory of a model operator and the proof of the theorem on expansion in terms of eigenfunctions. The imbedding mentioned is achieved by constructing a selfadjoint dilation $\mathscr L$ of the operator $L$. In the so-called incoming spectral representation of this dilation the operator becomes the corresponding model operator. Next, a system of eigenfunctions of the dilation – the “radiating” eigenfunctions – is constructed. From these a canonical system of eigenfunctions for the absolutely continuous spectrum of the operator and its spectral projections are obtained by “orthogonal projection” onto $H$. Bibliography: 22 titles. 
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     author = {B. S. Pavlov},
     title = {Selfadjoint dilatation of the dissipative {Shr\"odinger} operator and its resolution in terms of eigenfunctions},
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     volume = {31},
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     url = {http://geodesic.mathdoc.fr/item/SM_1977_31_4_a2/}
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B. S. Pavlov. Selfadjoint dilatation of the dissipative Shrödinger operator and its resolution in terms of eigenfunctions. Sbornik. Mathematics, Tome 31 (1977) no. 4, pp. 457-478. http://geodesic.mathdoc.fr/item/SM_1977_31_4_a2/

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