The setting of the Banach Gelfand triple (S0,L2,SO') allows to describe in a clean functional analytic way how a given continuous problem (such as applying a pseudo-differential operator given by its Kohn-Nirenberg symbol that should be applied to a given L2-function, or finding the spreading function of an operator) can be approximated at least in a qualitative way in a constructive way. The setting involves the use of function spaces, Fourier transforms and generalized functions, and aims at the reduction of a continuous problem to a finite-dimensional setting, which in principle is available for numerical implementation, e.g. using MATLAB or any other mathematical software.