EFFECT OF THE LONGITUDINAL MOMENTUM OF ELECTRONS ON THEIR SURFATRON ACCELERATION BY AN ELECTROMAGNETIC WAVE IN SPACE PLASMA
Plasma Physics Reports. Том 40. 2014. С. 812-819
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. © 2014, Springer Science+Business Media New York.