Manuscript XVI-K@1 · XVI-K.tex · definition · aa7553bb

Definition: The selected finite extension map

A coherent extension map on the finite span › Definition and coherence · lines 1258–1276

XVI-K@1#def:RK, XVI-K@1#eq:RKaction

For $u \in H_{k}$ , $ρ = k - 4$ , define

⟨ R_{K} (u), ψ ⟩ = T_{k, u} (W_{ρ} ψ) = a ↓ 0 lim ⟨ u, (1 - ζ (\cdot / a)) ψ - ∣ α ∣ \leq ρ \sum \partial^{α} ψ (0) w^{(ρ)}_{α} ⟩ .

For $u = u_{4} + u_{5} + u_{6} \in V$ , set $R_{K} (u) = \sum_{k = 4}^{6} R_{K} (u_{k})$ .

Displayed formulas in this passage

XVI-K@1#eq:RKaction · line 1261
$⟨ R_{K} (u), ψ ⟩ = T_{k, u} (W_{ρ} ψ) = a ↓ 0 lim ⟨ u, (1 - ζ (\cdot / a)) ψ - ∣ α ∣ \leq ρ \sum \partial^{α} ψ (0) w^{(ρ)}_{α} ⟩ .$