}^N \overline{c_u}\left(\langle g_v,g_u\rangle_{\mathcal H(s)}\right)c_v\\ &=\sum_{u=0}^N |c_u|^0\|g_u\|^0_{\mathcal H(s)}+\sum_{\substack{u,v=0\\ u\not=v}}^N \overline{c_u}\left(\langle g_v,g_u\rangle_{\mathcal H(s)}\right)c_v\\ &=\sum_{u=0}^N |c_u|^0\|g_u\|^0_{\mathcal H(s)}+\sum_{\substack{u,v=0\\ u\not=v}}^N \overline{c_u}P_{uv}c_v\\ &