\begin{equation}
	P_{\overline{\mathcal{H}}}f=\sum_{n\in J}\left\langle f,a_{n}\right\rangle_{\mathcal{L}_2^\nu}
	a_{n}\qquad\text{and}\qquad\left\langle P_{\overline{\mathcal{H}}}%
	f,a_{m}\right\rangle_{\mathcal{L}_2^\nu} =\left\langle f,a_{m}\right\rangle_{\mathcal{L}_2^\nu} ,\quad m\in
	J,\label{QRef}%
\end{equation}
