Theorem — If a tempered distribution f ∈ ∈ S ′ ( R d ) is such that e π π | x | 2 f ∈ ∈ S ′ ( R d ) and e π π | ξ ξ | 2 f ^ ^ ∈ ∈ S ′ ( R d ) , then f ( x ) = P ( x ) e − − π π ⟨ ⟨ A x , x ⟩ ⟩ , for some convenient polynomial P and real positive definite matrix A of type d × d.