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Sibirskii Matematicheskii Zhurnal, 2018, Volume 59, Number 3, Pages 596–615
DOI: https://doi.org/10.17377/smzh.2018.59.310 (Mi smj2997) 		 
This article is cited in 6 scientific papers (total in 6 papers)

A one-dimensional Schrödinger operator with square-integrable potential

D. M. Polyakovab

a Southern Mathematical Institute, Vladikavkaz, Russia
b Institute of Mathematics, Ufa, Russia
Full-text PDF (381 kB) Citations (6)
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DOI: https://doi.org/10.17377/smzh.2018.59.310
Abstract: We study the spectral properties of a one-dimensional Schrödinger operator with squareintegrable potential whose domain is defined by the Dirichlet boundary conditions. The main results are concerned with the asymptotics of the eigenvalues, the asymptotic behavior of the operator semigroup generated by the negative of the differential operator under consideration. Moreover, we derive deviation estimates for the spectral projections and estimates for the equiconvergence of the spectral decompositions. Our asymptotic formulas for eigenvalues refine the well-known ones.
Keywords: one-dimensional Schrödinger operator, asymptotics of the eigenvalues, spectral projection, operator semigroup.
Funding agency Grant number
Russian Foundation for Basic Research 16-31-00027
The author was supported by the Russian Foundation for Basic Research (Grant 16-31-00027).
Received: 06.04.2017
English version:
Siberian Mathematical Journal, 2018, Volume 59, Issue 3, Pages 470–485
DOI: https://doi.org/10.1134/S0037446618030102
Bibliographic databases:
Document Type: Article
UDC: 517.927
MSC: 35R30
Language: Russian
Citation: D. M. Polyakov, “A one-dimensional Schrödinger operator with square-integrable potential”, Sibirsk. Mat. Zh., 59:3 (2018), 596–615; Siberian Math. J., 59:3 (2018), 470–485
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский математический журнал Siberian Mathematical Journal
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