Differential Calculus on h-Deformed Spaces

We construct the rings of generalized differential operators on the h-deformed vector space of gl-type. In contrast to the q-deformed vector space, where the ring of differential operators is unique up to an isomorphism, the general ring of h-deformed differential operators Diff(h,sigma)(n) is labeled by a rational function sigma in n variables, satisfying an over-determined system of finite-difference equations. We obtain the general solution of the system and describe some properties of the rings Diff (h,sigma)(n).