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Mathematics of the USSR-Sbornik, 1977, Volume 31, Issue 4, Pages 457–478
DOI: https://doi.org/10.1070/SM1977v031n04ABEH003716
(Mi sm2695)
 

This article is cited in 49 scientific papers (total in 49 papers)

Selfadjoint dilatation of the dissipative Shrödinger operator and its resolution in terms of eigenfunctions

B. S. Pavlov
References:
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
Bibliographic databases:
UDC: 517.43
MSC: Primary 35J10, 35P10, 47A20; Secondary 47B44, 35P25
Language: English
Original paper language: Russian
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
Citation in format AMSBIB
\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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\zmath{https://zbmath.org/?q=an:0356.47007|0388.47003}
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  • https://doi.org/10.1070/SM1977v031n04ABEH003716
  • https://www.mathnet.ru/eng/sm/v144/i4/p511
  • This publication is cited in the following 49 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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