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Ufimskii Matematicheskii Zhurnal, 2012, Volume 4, Issue 2, Pages 65–73 (Mi ufa147)  

This article is cited in 7 scientific papers (total in 7 papers)

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
Full-text PDF (267 kB) Citations (7)
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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.
Received: 10.01.2012
Bibliographic databases:
Document Type: Article
UDC: 517.984
Language: Russian
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://mathscinet.ams.org/mathscinet-getitem?mr=3432643}
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  • This publication is cited in the following 7 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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