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Ufa Mathematical Journal, 2015, Volume 7, Issue 2, Pages 33–54
DOI: https://doi.org/10.13108/2015-7-2-33 (Mi ufa277) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Initial length scale estimate for waveguides with some random singular potentials

D.I. Borisovabc, R. Kh. Karimovb, T. F. Sharapovb

a University of Hradec Králové, Rokitanskeho, 62, 50003, Hradec Králové, Czech Republic
b Bashkir State Pedagogical University named after M. Akhmulla, October rev. st., 3a, 450000, Ufa, Russia
c Institute of Mathematics CC USC RAS, Chernyshevskii str., 112, 450008, Ufa, Russia
English version PDF (636 kB) Citations (6) Russian version article
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DOI: https://doi.org/10.13108/2015-7-2-33
Abstract: In this work we consider three examples of random singular perturbations in multi-dimensional models of waveguides. These perturbations are described by a large potential supported on a set of a small measure, by a compactly supported fast oscillating potential, and by a delta-potential. In all cases we prove initial length scale estimate.
Keywords: random operator, initial length scale estimate, perturbation, small parameter, spectral localization.
Received: 19.02.2015
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: 35P15, 35C20, 35B25, 60H25, 82B44
Language: English
Original paper language: Russian
Citation: D.I. Borisov, R. Kh. Karimov, T. F. Sharapov, “Initial length scale estimate for waveguides with some random singular potentials”, Ufa Math. J., 7:2 (2015), 33–54
Citation in format AMSBIB
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\by D.I.~Borisov, R.~Kh.~Karimov, T.~F.~Sharapov
\paper Initial length scale estimate for waveguides with some random singular potentials
\jour Ufa Math. J.
\yr 2015
\vol 7
\issue 2
\pages 33--54
\mathnet{http://mi.mathnet.ru/eng/ufa277}
\crossref{https://doi.org/10.13108/2015-7-2-33}
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\elib{https://elibrary.ru/item.asp?id=24188343}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84937828691}
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  • https://www.mathnet.ru/eng/ufa/v7/i2/p35
    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Уфимский математический журнал
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    Abstract page:561
    Russian version PDF:192
    English version PDF:21
    References:55
     
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