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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
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.
Received: 20.01.2022
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
Linking options:
https://www.mathnet.ru/eng/mzm13426https://doi.org/10.4213/mzm13426 https://www.mathnet.ru/eng/mzm/v111/i5/p692
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Abstract page: | 296 | Full-text PDF : | 30 | References: | 43 | First page: | 16 |
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