Conditions for the nonisomorphism of a pair of weighted spaces of continuous functions

In this paper, we formulate conditions for a pair of Fréchet spaces to be nonisomorphic. These conditions are formulated in terms of invariant classes of the spaces $(D_1)$ and $(D_2)$. As a consequence, we prove that weighted spaces of continuous functions of a special form are nonisomorphic. These spaces can be considered as a modification of spaces of power series of finite and infinite type.