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Mathematical Notes

, Volume 90, Issue 5–6, pp 701–714 | Cite as

On the index of nonlocal elliptic operators corresponding to a nonisometric diffeomorphism

  • A. Yu. SavinEmail author
Article

Abstract

We consider nonlocal elliptic operators corresponding to diffeomorphisms of smooth closed manifolds. The index of such operators is calculated. More precisely, it was shown that the index of the operator is equal to that of an elliptic boundary-value problem on the cylinder whose base is the original manifold. As an example, we study nonlocal operators on the two-dimensional Riemannian manifold corresponding to the tangential Euler operator.

Keywords

nonlocal elliptic operator index of an elliptic operator Riemannian manifold boundary-value problem diffeomorphism tangential Euler operator Fredholm property de Rham cohomology operators with shifts 

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Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  1. 1.Peoples’ Friendship University of RussiaMoscowRussia

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