Let $g \in C_{b}(\mathbb{R})$ with $N_{g}$ of finite codimension in $L^{1}(\mathbb{R})$. The functions $h_{r}$ are those from question I.D.3. Show that for $r$ sufficiently large the dimension of $V_{h_{r} * g}$ is equal to that of $V_{g}$.
Let $g \in C_{b}(\mathbb{R})$ with $N_{g}$ of finite codimension in $L^{1}(\mathbb{R})$. The functions $h_{r}$ are those from question I.D.3.\\
Show that for $r$ sufficiently large the dimension of $V_{h_{r} * g}$ is equal to that of $V_{g}$.