  We consider a distributed system of a type which is encountered in the study
of diffusion processes with memory and in viscoelasticity. The key feature of
such system is the persistence in the future of the past actions due the memory
described via a certain relaxation kernel, see below.
  The parameters of the kernel have to be inferred from experimental
measurements. Our main result in this paper is that by using two boundary
measurements the identification of a relaxation kernel which is linear
combination of Abel kernels (as often assumed in applications) can be reduced
to the solution of a (linear) deconvolution problem.
