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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)
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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
Russian version:
Ufimskii Matematicheskii Zhurnal, 2015, Volume 7, Issue 2, Pages 35–56
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”, Ufimsk. Mat. Zh., 7:2 (2015), 35–56; Ufa Math. J., 7:2 (2015), 33–54
Citation in format AMSBIB
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\pages 35--56
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  • https://doi.org/10.13108/2015-7-2-33
  • 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:499
    Russian version PDF:163
    English version PDF:8
    References:41
     
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