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Ufimsk. Mat. Zh., 2015, Volume 7, Issue 2, Pages 35–56 (Mi ufa277)  

This article is cited in 4 scientific papers (total in 4 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

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.

Full text: PDF file (687 kB)
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English version:
Ufa Mathematical Journal, 2015, 7:2, 33–54 (PDF, 636 kB); https://doi.org/10.13108/2015-7-2-33

Bibliographic databases:

UDC: 517.9
MSC: 35P15, 35C20, 35B25, 60H25, 82B44
Received: 19.02.2015

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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\by D.I.~Borisov, R.~Kh.~Karimov, T.~F.~Sharapov
\paper Initial length scale estimate for waveguides with some random singular potentials
\jour Ufimsk. Mat. Zh.
\yr 2015
\vol 7
\issue 2
\pages 35--56
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\jour Ufa Math. J.
\yr 2015
\vol 7
\issue 2
\pages 33--54
\crossref{https://doi.org/10.13108/2015-7-2-33}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. R. Bikmetov, V. F. Vil'danova, I. Kh. Khusnullin, “On perturbation of a Schrödinger operator on axis by narrow potentials”, Ufa Math. J., 7:4 (2015), 24–31  mathnet  crossref  isi  elib
    2. A. R. Bikmetov, I. Kh. Khusnullin, “Perturbation of Hill operator by narrow potentials”, Russian Math. (Iz. VUZ), 61:7 (2017), 1–10  mathnet  crossref  isi
    3. I. Kh. Khusnullin, “Vozmuschenie volnovoda uzkim potentsialom”, Tr. IMM UrO RAN, 23, no. 2, 2017, 274–284  mathnet  crossref  elib
    4. D. Borisov, F. Hoecker-Escuti, I. Veselic, “Expansion of the spectrum in the weak disorder regime for random operators in continuum space”, Commun. Contemp. Math., 20:1 (2018), 1750008  crossref  mathscinet  zmath  isi  scopus
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