Elliptic translators on manifolds with multidimensional singularities

We consider translators on manifolds with many-dimensional singularities. We state the definition of ellipticity for translators, prove a finiteness (Fredholm property) theorem, and establish an index formula.     

Index problem for elliptic operators associated with a diffeomorphism of a manifold and uniformization

Doklady Mathematics -     

Index of nonlocal problems associated with a bundle

We study operators associated with a bundle with compact base and fiber. We construct an algebra of such operators. For elliptic elements of the algebra, we prove the finiteness theorem and derive an index formula.     

On the Index Formula for an Isometric Diffeomorphism

We give an elementary solution to the problem of the index of elliptic operators associated with shift operator along the trajectories of an isometric diffeomorphism of a smooth closed manifold. This solution is based on index-preserving reduction of the operator under consideration to some elliptic pseudo-differential operator on a higher-dimension manifold and on the application of the Atiyah–Singer formula. The final formula of the index is given in terms of the symbol of the operator on the original manifold.