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

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autoren

  • A. Baldare
  • V. E. Nazaikinskii
  • A. Yu Savin
  • E. Schrohe

Organisationseinheiten

Externe Organisationen

  • RAS - Institute for Problems in Mechanics
  • Peoples' Friendship University of Russia (RUDN)
Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Seiten (von - bis)701-721
Seitenumfang21
FachzeitschriftMathematical notes
Jahrgang111
Ausgabenummer5
Frühes Online-Datum23 Juni 2022
PublikationsstatusVeröffentlicht - Juni 2022

Abstract

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.

ASJC Scopus Sachgebiete

Zitieren

C-Algebras of Transmission Problems and Elliptic Boundary Value Problems with Shift Operators. / Baldare, A.; Nazaikinskii, V. E.; Savin, A. Yu et al.
in: Mathematical notes, Jahrgang 111, Nr. 5, 06.2022, S. 701-721.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Baldare A, Nazaikinskii VE, Savin AY, Schrohe E. C-Algebras of Transmission Problems and Elliptic Boundary Value Problems with Shift Operators. Mathematical notes. 2022 Jun;111(5):701-721. Epub 2022 Jun 23. doi: 10.1134/S0001434622050042
Baldare, A. ; Nazaikinskii, V. E. ; Savin, A. Yu et al. / C-Algebras of Transmission Problems and Elliptic Boundary Value Problems with Shift Operators. in: Mathematical notes. 2022 ; Jahrgang 111, Nr. 5. S. 701-721.
Download
@article{9e70675d4ed742cb9cd34707f9c8b5eb,
title = "C-Algebras of Transmission Problems and Elliptic Boundary Value Problems with Shift Operators",
abstract = "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 = "C-algebra, crossed product, ellipticity, Fredholm property, group action, manifold with boundary, nonlocal operator",
author = "A. Baldare and Nazaikinskii, {V. E.} and Savin, {A. Yu} and E. Schrohe",
note = "Funding Information: 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).",
year = "2022",
month = jun,
doi = "10.1134/S0001434622050042",
language = "English",
volume = "111",
pages = "701--721",
journal = "Mathematical notes",
issn = "0001-4346",
publisher = "Pleiades Publishing",
number = "5",

}

Download

TY - JOUR

T1 - C-Algebras of Transmission Problems and Elliptic Boundary Value Problems with Shift Operators

AU - Baldare, A.

AU - Nazaikinskii, V. E.

AU - Savin, A. Yu

AU - Schrohe, E.

N1 - Funding Information: 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).

PY - 2022/6

Y1 - 2022/6

N2 - 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.

AB - 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.

KW - C-algebra

KW - crossed product

KW - ellipticity

KW - Fredholm property

KW - group action

KW - manifold with boundary

KW - nonlocal operator

UR - http://www.scopus.com/inward/record.url?scp=85132842090&partnerID=8YFLogxK

U2 - 10.1134/S0001434622050042

DO - 10.1134/S0001434622050042

M3 - Article

AN - SCOPUS:85132842090

VL - 111

SP - 701

EP - 721

JO - Mathematical notes

JF - Mathematical notes

SN - 0001-4346

IS - 5

ER -