Sampling of vector-valued transforms associated with Green’s matrix of Dirac systems

Recently a sampling theorem associated with regular one-dimensional Dirac systems has been developed. Integral transforms whose kernels are solutions of the systems have been reconstructed from their values at the eigenvalues. In the present article the situation is considered where the kernels are replaced by Green’s matrix of the problem. Thus a vector-valued sampling theorem is established for vector-valued transforms. A family of examples where the systems have variable coefficients and a vector-valued Kramer-type sampling lemma are given at the end of the paper.  2003 Published by Elsevier Inc.