Details
| Original language | English |
|---|---|
| Pages (from-to) | 410-420 |
| Number of pages | 11 |
| Journal | Russian Journal of Mathematical Physics |
| Volume | 22 |
| Issue number | 3 |
| Publication status | Published - 2 Sept 2015 |
Abstract
We consider the index problem for a wide class of nonlocal elliptic operators on a smooth closed manifold, namely, differential operators with shifts induced by the action of a (not necessarily periodic) isometric diffeomorphism. The key to the solution is the method of uniformization. To the nonlocal problem we assign a pseudodifferential operator, with the same index, acting on the sections of an infinite-dimensional vector bundle on a compact manifold. We then determine the index in terms of topological invariants of the symbol, using the Atiyah—Singer index theorem.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematics(all)
- Mathematical Physics
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In: Russian Journal of Mathematical Physics, Vol. 22, No. 3, 02.09.2015, p. 410-420.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Uniformization and index of elliptic operators associated with diffeomorphisms of a manifold
AU - Savin, A.
AU - Schrohe, E.
AU - Sternin, B.
N1 - Publisher Copyright: © 2015, Pleiades Publishing, Ltd. Copyright: Copyright 2015 Elsevier B.V., All rights reserved.
PY - 2015/9/2
Y1 - 2015/9/2
N2 - We consider the index problem for a wide class of nonlocal elliptic operators on a smooth closed manifold, namely, differential operators with shifts induced by the action of a (not necessarily periodic) isometric diffeomorphism. The key to the solution is the method of uniformization. To the nonlocal problem we assign a pseudodifferential operator, with the same index, acting on the sections of an infinite-dimensional vector bundle on a compact manifold. We then determine the index in terms of topological invariants of the symbol, using the Atiyah—Singer index theorem.
AB - We consider the index problem for a wide class of nonlocal elliptic operators on a smooth closed manifold, namely, differential operators with shifts induced by the action of a (not necessarily periodic) isometric diffeomorphism. The key to the solution is the method of uniformization. To the nonlocal problem we assign a pseudodifferential operator, with the same index, acting on the sections of an infinite-dimensional vector bundle on a compact manifold. We then determine the index in terms of topological invariants of the symbol, using the Atiyah—Singer index theorem.
UR - http://www.scopus.com/inward/record.url?scp=84940864046&partnerID=8YFLogxK
U2 - 10.1134/S1061920815030115
DO - 10.1134/S1061920815030115
M3 - Article
AN - SCOPUS:84940864046
VL - 22
SP - 410
EP - 420
JO - Russian Journal of Mathematical Physics
JF - Russian Journal of Mathematical Physics
SN - 1061-9208
IS - 3
ER -