Details
| Original language | English |
|---|---|
| Pages (from-to) | 846-849 |
| Number of pages | 4 |
| Journal | Doklady mathematics |
| Volume | 84 |
| Issue number | 3 |
| Publication status | Published - 5 Jan 2012 |
Abstract
Index problem for elliptic operators associated with a diffeomorphism of a manifold and uniformization was studied. Let M be a smooth manifold on which a smooth isometric diffeomorphism g: M → M is given. The powers of this diffeomorphism generate an action of the group &Zdbl; on the manifold. The method for solving this problem in pseudodifferentially uniformizing the operator D, reducing this operator to some elliptic differential operator whose index coincides with the index of the original operator. The reduction is performed in two stages. The first stage consists in replacing the manifold M by the manifold M × &Rdbl; with the diagonal action of the group &Zdbl;. At the second stage, the obtained operator on M × &Rdbl; as a differential operator on the sections of an infinite-dimensional bundle on the smooth manifold.
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Doklady mathematics, Vol. 84, No. 3, 05.01.2012, p. 846-849.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Index Problem for Elliptic Operators Associated with a Diffeomorphism of a Manifold and Uniformization
AU - Savin, A. Yu
AU - Sternin, B. Yu
AU - Schrohe, E.
N1 - Funding Information: This work was supported by DFG (project no. 436 RUS 113/849/0 1®). Copyright: Copyright 2012 Elsevier B.V., All rights reserved.
PY - 2012/1/5
Y1 - 2012/1/5
N2 - Index problem for elliptic operators associated with a diffeomorphism of a manifold and uniformization was studied. Let M be a smooth manifold on which a smooth isometric diffeomorphism g: M → M is given. The powers of this diffeomorphism generate an action of the group &Zdbl; on the manifold. The method for solving this problem in pseudodifferentially uniformizing the operator D, reducing this operator to some elliptic differential operator whose index coincides with the index of the original operator. The reduction is performed in two stages. The first stage consists in replacing the manifold M by the manifold M × &Rdbl; with the diagonal action of the group &Zdbl;. At the second stage, the obtained operator on M × &Rdbl; as a differential operator on the sections of an infinite-dimensional bundle on the smooth manifold.
AB - Index problem for elliptic operators associated with a diffeomorphism of a manifold and uniformization was studied. Let M be a smooth manifold on which a smooth isometric diffeomorphism g: M → M is given. The powers of this diffeomorphism generate an action of the group &Zdbl; on the manifold. The method for solving this problem in pseudodifferentially uniformizing the operator D, reducing this operator to some elliptic differential operator whose index coincides with the index of the original operator. The reduction is performed in two stages. The first stage consists in replacing the manifold M by the manifold M × &Rdbl; with the diagonal action of the group &Zdbl;. At the second stage, the obtained operator on M × &Rdbl; as a differential operator on the sections of an infinite-dimensional bundle on the smooth manifold.
UR - http://www.scopus.com/inward/record.url?scp=84856955338&partnerID=8YFLogxK
U2 - 10.1134/S1064562411070350
DO - 10.1134/S1064562411070350
M3 - Article
AN - SCOPUS:84856955338
VL - 84
SP - 846
EP - 849
JO - Doklady mathematics
JF - Doklady mathematics
SN - 1064-5624
IS - 3
ER -