Voprosy Obrazovaniya.
National Research University Higher School of Economics.
Vol. 2012.
2012.
P. 165-183
We investigate nonlocal operators associated with the operators of compression and expansion. We obtain an ellipticity condition, which implies that the problem has the Fredholm property, compute the index, and study how the index depends on the exponent of the Sobolev space in which the problem is considered. © 2011 RAS(DoM) and LMS.