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 dimensions of the kernel and cokernel is obtained. The key point is the splitting of the operator obtained by using spectral projectors of the Laplace operator in the bounded transverse domain. This, together with a continuation method, allows the reduction to one dimensional systems for which the index may be computed explicitly.