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Matematicheskie Zametki, 2022, Volume 111, Issue 5, Pages 692–716
DOI: https://doi.org/10.4213/mzm13426
(Mi mzm13426)
 

This article is cited in 2 scientific papers (total in 2 papers)

$C^*$-Algebras of Transmission Problems and Elliptic Boundary Value Problems with Shift Operators

A. Baldarea, V. E. Nazaikinskiib, A. Yu. Savinc, E. Schrohea

a Institute of Analysis, Leibniz University Hannover
b Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow
c Peoples' Friendship University of Russia, Moscow
Full-text PDF (715 kB) Citations (2)
References:
Abstract: We study the Fredholm solvability for a new class of nonlocal boundary value problems associated with group actions on smooth manifolds. Namely, we consider the case in which the group action is defined on an ambient manifold without boundary and does not preserve the manifold with boundary on which the problem is stated. In particular, the group action does not map the boundary into itself. The orbits of the boundary under the group action split the manifold into subdomains, and this decomposition, being combined with the $C^*$-algebra techniques, plays an important role in our approach to the analysis of the problem.
Keywords: manifold with boundary, nonlocal operator, group action, ellipticity, Fredholm property, $C^*$-algebra, crossed product.
Funding agency Grant number
Russian Foundation for Basic Research 21-51-12006
Deutsche Forschungsgemeinschaft SCHR 319/10-1
This work was supported by the Russian Foundation for Basic Research under grant 21-51-12006 and by the Deutsche Forschungsgemeinschaft (project SCHR 319/10-1).
Received: 20.01.2022
English version:
Mathematical Notes, 2022, Volume 111, Issue 5, Pages 701–721
DOI: https://doi.org/10.1134/S0001434622050042
Bibliographic databases:
Document Type: Article
UDC: 517.968
Language: Russian
Citation: A. Baldare, V. E. Nazaikinskii, A. Yu. Savin, E. Schrohe, “$C^*$-Algebras of Transmission Problems and Elliptic Boundary Value Problems with Shift Operators”, Mat. Zametki, 111:5 (2022), 692–716; Math. Notes, 111:5 (2022), 701–721
Citation in format AMSBIB
\Bibitem{BalNazSav22}
\by A.~Baldare, V.~E.~Nazaikinskii, A.~Yu.~Savin, E.~Schrohe
\paper $C^*$-Algebras of Transmission Problems and Elliptic Boundary Value Problems with Shift Operators
\jour Mat. Zametki
\yr 2022
\vol 111
\issue 5
\pages 692--716
\mathnet{http://mi.mathnet.ru/mzm13426}
\crossref{https://doi.org/10.4213/mzm13426}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4461299}
\transl
\jour Math. Notes
\yr 2022
\vol 111
\issue 5
\pages 701--721
\crossref{https://doi.org/10.1134/S0001434622050042}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85132842090}
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  • https://www.mathnet.ru/eng/mzm13426
  • https://doi.org/10.4213/mzm13426
  • https://www.mathnet.ru/eng/mzm/v111/i5/p692
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Математические заметки Mathematical Notes
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