The index problem for nonlocal elliptic operators representable as a finite sum of the form of pseudodifferential operators is studied. Index formulas for operators are obtained for special diffeomorphisms and the index of operators corresponding to a linear shift on the torus are calculated. Topological invariants of nonlocal elliptic operators for diffeomorphism of general form are constructed and the analytic index of an operator in terms of these invariants is expressed. An operator is said to be elliptic if, for this operator, there exists an inverse symbol with finitely many nonzero components. The Chern character on the K-group of crossed products with the group is defined. For an elliptic operator, the Chern character with values in the Haefliger cohomology are defined.

Authors

Journal

Number of issue

3

Language

English

Pages

353-356

Status

Published

Link

Volume

83

Year

2011

Organizations

^{1}Peoples Friendship University, ul. Miklukho-Maklaya 6, Moscow 117198, Russian Federation^{2}Leibniz University of Hannover, Hannover, Germany

Date of creation

19.10.2018

Date of change

19.10.2018

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