Inverse spectral problem for the Laguerre differential operator

We construct a self-adjoint operator associated with the following given set of eigenvalues: {an + c}(n) (less than or equal to) (-1) boolean OR {an + b}(n greater than or equal to 0). This problem arises in sampling theory and deals with the construction of an interpolating basis associated with a given set of sampling points, the so-called two sided cardinal series. In order to solve this inverse spectral problem we shall need to extend the Gelfand-Levitan theory to operators close to the Laguerre differential operator. (C) 1998 Academic Press.