Manuscript XV-D@1 · XV-D.tex · definition · 967136eb

Definition: Full and punctured reconstruction

The null defect in the one source-complete module › Chart, insertions, and two reconstructions · lines 672–687

XV-D@1#def:tworec

Fix $T^{\circ} \in D^{'} (X^{\circ})$ . The punctured reconstruction is

Rec^{\circ} : P_{r}^{jet} ⟶ D^{'} (U^{\circ}), Rec^{\circ} (a) = ∣ α ∣ \leq r \sum a_{α} ∣_{U^{\circ}} E^{\circ}_{α} T^{\circ} .

For an extension $T \in D^{'} (X)$ of $T^{\circ}$ (that is, $T ∣_{X^{\circ}} = T^{\circ}$ ), the full reconstruction is

Rec_{T} : P_{r}^{jet} ⟶ D^{'} (U), Rec_{T} (a) = ∣ α ∣ \leq r \sum a_{α} E_{α} T .

Write $H = ker Rec^{\circ}$ and $H_{T} = ker Rec_{T}$ .

Displayed formulas in this passage

unlabeled · line 675
$Rec^{\circ} : P_{r}^{jet} ⟶ D^{'} (U^{\circ}), Rec^{\circ} (a) = ∣ α ∣ \leq r \sum a_{α} ∣_{U^{\circ}} E^{\circ}_{α} T^{\circ} .$
unlabeled · line 682
$Rec_{T} : P_{r}^{jet} ⟶ D^{'} (U), Rec_{T} (a) = ∣ α ∣ \leq r \sum a_{α} E_{α} T .$