Manuscript Em01-A@1 · Em01-A.tex · section · 880b67af

Support and normal order must be explicit

A precise supported normal-jet interface › Support and normal order must be explicit · lines 1168–1189

Em01-A@1#eq:jet-insertion

Let

U = S_{0} \times R^{k}, S = S_{0} \times {0},

where $S_{0} \subseteq R^{d}$ is open. Write coordinates as $(s, z)$ . Let $A \subseteq S_{0}$ be relatively closed, and set

N = A \times {0}, U^{\circ} = U ∖ N .

For a multi-index $γ \in N^{k}$ , define

⟨ E_{γ} b, φ ⟩ = (- 1)^{∣ γ ∣} ⟨ b, \partial_{z}^{γ} φ (s, 0)⟩, b \in D^{'} (S_{0}) .

Thus $E_{γ} b = b \otimes \partial_{z}^{γ} δ_{0}$ .

Displayed formulas in this passage

unlabeled · line 1171
$U = S_{0} \times R^{k}, S = S_{0} \times {0},$
unlabeled · line 1176
$N = A \times {0}, U^{\circ} = U ∖ N .$
Em01-A@1#eq:jet-insertion · line 1181
$⟨ E_{γ} b, φ ⟩ = (- 1)^{∣ γ ∣} ⟨ b, \partial_{z}^{γ} φ (s, 0)⟩, b \in D^{'} (S_{0}) .$