  Viscoelastic materials have non-negative relaxation spectra. This property
implies that viscoelastic response functions satisfy certain necessary and
sufficient conditions. It is shown that these conditions can be expressed in
terms of each viscoelastic response function ranging over a cone. The elements
of each cone are completely characterized by an integral representation. The
1:1 correspondences between the viscoelastic response functions are expressed
in terms of cone-preserving mappings and their inverses. The theory covers
scalar and tensor-valued viscoelastic response functions
