  The first focus of this paper is the characterization of the spectrum and the
singular values of the coefficient matrix stemming from the discretization with
space-time grid for a parabolic diffusion problem and from the approximation of
distributed order fractional equations. For this purpose we will use the
classical GLT theory and the new concept of GLT momentary symbols. The first
permits to describe the singular value or eigenvalue asymptotic distribution of
the sequence of the coefficient matrices, the latter permits to derive a
function, which describes the singular value or eigenvalue distribution of the
matrix of the sequence, even for small matrix-sizes but under given
assumptions. The note is concluded with a list of open problems, including the
use of our machinery in the study of iteration matrices, especially those
concerning multigrid-type techniques.
