Manuscript XI-G@1 · XI-G.tex · section · f029bbcd

G2: the separation lemma

G2: the separation lemma · lines 855–872

XI-G@1#eq:Ideal

Throughout,

I_{sol} := □_{1} E^{'} + □_{2} E^{'} + P_{m, 3} E^{'}, W_{w} := E_{0, 1} E_{0, 2} E_{m, 3} w = (E_{0} \otimes E_{0} \otimes E_{m}) w (w \in E^{'}),

the bulk equation ideal and the trisolution of $w$ . The trisolution is a distribution on $M^{3}$ solving $□_{1} W_{w} = □_{2} W_{w} = P_{m, 3} W_{w} = 0$ , with support in $J (K_{1}) \times J (K_{2}) \times J (K_{3})$ , $K_{i}$ the projection of $supp w$ to slot $i$ and $J = J^{+} \cup J^{-}$ ; its support is compact in each slot over every bounded time interval.

Displayed formulas in this passage

XI-G@1#eq:Ideal · line 859
$I_{sol} := □_{1} E^{'} + □_{2} E^{'} + P_{m, 3} E^{'}, W_{w} := E_{0, 1} E_{0, 2} E_{m, 3} w = (E_{0} \otimes E_{0} \otimes E_{m}) w (w \in E^{'}),$