Geodesic
$C^*$-Algebras of Transmission Problems and Elliptic Boundary Value Problems with Shift Operators
Matematičeskie zametki, Tome 111 (2022) no. 5, pp. 692-716

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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, ellipticity, Fredholm property, $C^*$-algebra, crossed product.
Mots-clés : group action 
@article{MZM_2022_111_5_a3,
     author = {A. Baldare and V. E. Nazaikinskii and A. Yu. Savin and E. Schrohe},
     title = {$C^*${-Algebras} of {Transmission} {Problems} and {Elliptic} {Boundary} {Value} {Problems} with {Shift} {Operators}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {692--716},
     publisher = {mathdoc},
     volume = {111},
     number = {5},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2022_111_5_a3/}
}
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A. Baldare; V. E. Nazaikinskii; A. Yu. Savin; E. Schrohe. $C^*$-Algebras of Transmission Problems and Elliptic Boundary Value Problems with Shift Operators. Matematičeskie zametki, Tome 111 (2022) no. 5, pp. 692-716. http://geodesic.mathdoc.fr/item/MZM_2022_111_5_a3/