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.
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).
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
This publication is cited in the following 3 articles:
A. V. Boltachev, “On Ellipticity of Operators with Shear Mappings”, J Math Sci, 2024
A. V. Boltachev, “Ob elliptichnosti operatorov so skruchivaniyami”, SMFN, 69, no. 4, Rossiiskii universitet druzhby narodov, M., 2023, 565–577
A. V. Boltachev, A. Yu. Savin, “Trajectory symbols and the Fredholm property of boundary value problems for differential operators with shifts”, Russ. J. Math. Phys., 30:2 (2023), 135