Definition: Classical evaluation

For a smooth solution $u$ of $P_{m}u=0$, define ${\mathrm{ev}}_u:{{\mathfrak{A}}_0}^{(1)}\to \mathbb{C}$ by ${\mathrm{ev}}_u\hat{\varphi }(d)=⟨d,u⟩$. This is well defined by Lemma lem:detect, (a)$\Rightarrow$(d), and the family $\{{\mathrm{ev}}_u:u\in {\Delta }_S\mathcal{D}\}$ separates points of ${{\mathfrak{A}}_0}^{(1)}$ by Lemma lem:detect, (c)$\Rightarrow$(a).