\[\left\langle\mathscr{F}\left(P(\mathbf{D})u\right),\phi\right\rangle=\left%
\langle P_{-}\mathscr{F}\left(u\right),\phi\right\rangle=\left\langle\mathscr{%
F}\left(u\right),P_{-}\phi\right\rangle,\]