Description of the Duals of Subspaces of Infinitely Differentiable Functions

We describe spaces that are dual to some subspaces of the space C∞(D) relative to the inductive limits, where inductive limits, where D⊂ℝ^p is a bounded convex domain. For any logarithmically convex space of positive numbers ℳ={M_k,k∈ℤ_+^p} we introduce the normed space C(D,ℳ) of functions f∈C^∞(D) and prove that the Fourier-Laplace transform establishes a topological isomorphism between the strongly dual space and the projective limit of the normed spaces.