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Sbornik: Mathematics, 2017, Volume 208, Issue 2, Pages 269–284
DOI: https://doi.org/10.1070/SM8686 (Mi sm8686) 		 
This article is cited in 3 scientific papers (total in 3 papers)

An estimate for the number of eigenvalues of the Schrödinger operator with a complex potential

S. A. Stepin

Faculty of Mechanics and Mathematics, Lomonosov Moscow State University
English version PDF (457 kB) Citations (3)
References:
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DOI: https://doi.org/10.1070/SM8686
Abstract: For the Schrödinger operator whose potential is rapidly decreasing at infinity, an estimate for the number of eigenvalues is given, thus answering a question going back to Gelfand. The case of three-dimensional configuration space is chosen for simplicity of presentation; all the results formulated in the paper can be extended to an arbitrary number of degrees of freedom.
Bibliography: 19 titles.
Keywords: Schrödinger operator, Fredholm determinant, total multiplicity of eigenvalues.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00117-а
This research was carried out with the support of the Russian Foundation for Basic Research (grant no. 16-01-00117-a).
Received: 01.03.2016 and 24.10.2016
Russian version:
Matematicheskii Sbornik, 2017, Volume 208, Number 2, Pages 104–120
DOI: https://doi.org/10.4213/sm8686
Bibliographic databases:
Document Type: Article
UDC: 517.984.56
MSC: 35J10, 35P15
Language: English
Original paper language: Russian
Citation: S. A. Stepin, “An estimate for the number of eigenvalues of the Schrödinger operator with a complex potential”, Mat. Sb., 208:2 (2017), 104–120; Sb. Math., 208:2 (2017), 269–284
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математический сборник Sbornik: Mathematics
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    Russian version PDF:79
    English version PDF:24
    References:76
    First page:53
     
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