  We use a generalization of Wiener's $1/f$ theorem to prove that for a Gabor
frame with the generator in the Wiener amalgam space $W(L^{\infty},
\ell^{1}_{\nu})(\mathbb{R}^{d})$, the corresponding frame operator is
invertible on this space. Therefore, for such a Gabor frame, the generator of
the canonical dual belongs also to $W(L^{\infty},
\ell^{1}_{\nu})(\mathbb{R}^{d}) $
