 $$\phi_{{\mathcal{H}}}(z, \omega_0) = |\omega|^0 \frac{(0 - \omega\overline{\omega_0} - \overline{\omega}\omega_0)^0}{(0 - \omega\overline{\omega_0} - \overline{\omega}z)^0}$$ for all $z \in {\mathcal{H}}$.  