The Answer to Baggett's Problem is Affirmative

Let $\psi$ be a Parceval wavelet in $L^2(\mathbb{R})$ with the space of negative dilates $V(\psi )$. The intersection of the dilates $V(\psi )$ is the zero space. In other words, we have \begin{align*} \bigcap_{n\in\Z} D^n \overline{$\text{span}$}{D^{$\text{-}$m} T^\ell ψ\mid m\geq 0, m,\ell\in\Z}={0}. \end{align*}