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Ufimsk. Mat. Zh., 2012, Volume 4, Issue 2, Pages 65–73 (Mi ufa147)  

This article is cited in 1 scientific paper (total in 1 paper)

On the resolvents of periodic operators with distant perturbations

D. I. Borisovab, A. M. Golovinaa

a Bashkir State Pedagogical University, Ufa, Russia
b Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa, Russia

Abstract: We consider distant perturbations for an abstract periodic operator. The unperturbed operator is introduced as a closed operator on the Sobolev space defined on a periodic domain in a multidimensional space. We impose certain condition for the unperturbed operator being a natural generalization of the ellipticity and periodicity conditions for the differential operators. The perturbations are described by abstract relatively bounded operators being localized in a certain sense. We study the case when the distance between the domains, where the perturbations are localized, increases unboundedly. The main obtained result is the explicit representation for the resolvent of the perturbed operator.

Keywords: resolvent, periodic operator, distant perturbations.

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Bibliographic databases:
UDC: 517.984
Received: 10.01.2012

Citation: D. I. Borisov, A. M. Golovina, “On the resolvents of periodic operators with distant perturbations”, Ufimsk. Mat. Zh., 4:2 (2012), 65–73

Citation in format AMSBIB
\Bibitem{BorGol12}
\by D.~I.~Borisov, A.~M.~Golovina
\paper On the resolvents of periodic operators with distant perturbations
\jour Ufimsk. Mat. Zh.
\yr 2012
\vol 4
\issue 2
\pages 65--73
\mathnet{http://mi.mathnet.ru/ufa147}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3432643}


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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. Borisov D., Exner P., Golovina A., “Tunneling Resonances in Systems Without a Classical Trapping”, J. Math. Phys., 54:1 (2013), 012102  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
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