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Index of elliptic operators for diffeomorphisms of manifolds. (English) Zbl 1320.58010
The authors deal with operators that are obtained by iterates of a given diffeomorphism of a closed manifold $$M$$ composed with pseudo-differential operators on $$M$$ and finite sums of these. The algebra of symbols of those operators is noncommutative. An elliptic theory for such operators is developped. In particular, a notion of being elliptic is defined which implies Fredholmness and regularity properties of kernel and cokernel. An index formula in terms of topological invariants and the symbol of the operator is presented.

##### MSC:
 58J05 Elliptic equations on manifolds, general theory 19K56 Index theory 46L85 Noncommutative topology 58D05 Groups of diffeomorphisms and homeomorphisms as manifolds 58J40 Pseudodifferential and Fourier integral operators on manifolds 58J20 Index theory and related fixed-point theorems on manifolds
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