A generalized diffusion equation

A generalized space, Gamma(s,mu,M), and its dual are introduced where mu is a sequence of positive numbers, M is a space of continuous functions and s greater than or equal to 1. A generalized Laplacian operator, a, is introduced applied to functionals in Gamma(s,mu,M). Together with a classical time derivative the generalized diffusion equation is shown to have a local solution in a space, Gamma(s',mu,M) where s' greater than or equal to s.