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This article is cited in 48 scientific papers (total in 48 papers)
Selfadjoint dilatation of the dissipative Shrödinger operator and its resolution in terms of eigenfunctions
B. S. Pavlov
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.
Received: 11.03.1976
Citation:
B. S. Pavlov, “Selfadjoint dilatation of the dissipative Shrödinger operator and its resolution in terms of eigenfunctions”, Mat. Sb. (N.S.), 102(144):4 (1977), 511–536; Math. USSR-Sb., 31:4 (1977), 457–478
Linking options:
https://www.mathnet.ru/eng/sm2695https://doi.org/10.1070/SM1977v031n04ABEH003716 https://www.mathnet.ru/eng/sm/v144/i4/p511
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Abstract page: | 1014 | Russian version PDF: | 203 | English version PDF: | 12 | References: | 47 |
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