  We present a solution of the Weiss operator family generalized for the case
of $\mathbb{R}^{d}$ and formulate a d-dimensional analogue of the Weiss
Theorem. Most importantly, the generalization of the Weiss Theorem allows us to
find a sub-set of null class functions for a partial differential equation with
the generalized Weiss operators. We illustrate the significance of our approach
through several examples of both linear and non-linear partial differential
equations.
