Computation of the index of linear elliptic operators in unbounded cylinders

Linear Fredholm elliptic operators in unbounded cylinders are considered. A formula for the index of the operator, i.e., the difference between the di mensions of the kernel and cokernel is obtained. The key point is the split ting of the operator obtained by using spectral projectors of the Laplace o perator in the bounded transverse domain. This, together with a continuatio n method, allows the reduction to one dimensional systems for which the ind ex may be computed explicitly. (C) 1999 Academic Press.