Abstract:
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.
Citation:
B. S. Pavlov, “Selfadjoint dilatation of the dissipative Shrödinger operator and its resolution in terms of eigenfunctions”, Math. USSR-Sb., 31:4 (1977), 457–478
\Bibitem{Pav77}
\by B.~S.~Pavlov
\paper Selfadjoint dilatation of the dissipative Shr\"odinger operator and its resolution in terms of eigenfunctions
\jour Math. USSR-Sb.
\yr 1977
\vol 31
\issue 4
\pages 457--478
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\crossref{https://doi.org/10.1070/SM1977v031n04ABEH003716}
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Linking options:
https://www.mathnet.ru/eng/sm2695
https://doi.org/10.1070/SM1977v031n04ABEH003716
https://www.mathnet.ru/eng/sm/v144/i4/p511
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