  Let $G$ be a compact subgroup of $GL_n(\R)$ acting linearly on a finite
dimensional vector space $E$. B. Malgrange has shown that the space
$\mathcal{C}^\infty(\R^n,E)^G$ of $\mathcal{C}^\infty$ and $G$-covariant
functions is a finite module over the ring $\mathcal{C}^\infty(\R^n)^G$ of
$\mathcal{C}^\infty$ and $G$-invariant functions. First, we generalize this
result for the Schwartz space $\mathscr{S}(\R^n,E)^G$ of $G$-covariant
functions. Secondly, we prove that any $G$-covariant distribution can be
decomposed into a sum of $G$-invariant distributions multiplied with a fixed
family of $G$-covariant polynomials. This gives a generalization of an Oksak
result proved in ([O]).
