Geodesic
On the Index of Nonlocal Elliptic Operators Corresponding to a Nonisometric Diffeomorphism
Matematičeskie zametki, Tome 90 (2011) no. 5, pp. 712-726

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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 the 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 Euler tangent operator.
Keywords: nonlocal elliptic operator, index of an elliptic operator, Riemannian manifold, elliptic boundary-value problem, diffeomorphism, Euler tangent operator, ellipticity condition, Fredholm property. 
@article{MZM_2011_90_5_a6,
     author = {A. Yu. Savin},
     title = {On the {Index} of {Nonlocal} {Elliptic} {Operators} {Corresponding} to a {Nonisometric} {Diffeomorphism}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {712--726},
     publisher = {mathdoc},
     volume = {90},
     number = {5},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_90_5_a6/}
}
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A. Yu. Savin. On the Index of Nonlocal Elliptic Operators Corresponding to a Nonisometric Diffeomorphism. Matematičeskie zametki, Tome 90 (2011) no. 5, pp. 712-726. http://geodesic.mathdoc.fr/item/MZM_2011_90_5_a6/