Manuscript V-B@1 · V-B-v1.tex · section · 3fadc1ad

Green identities and compact smoothing

Admissibility on the declared solution spaces › Green identities and compact smoothing · lines 590–603

V-B@1#eq:compactprimitive

For a compact distribution $C$ ,

E_{r} C = 0 ⟺ G_{r, A} C = G_{r, R} C =: A_{C} is compact, □ A_{C} = C .

Indeed, the common support is contained in the compact causal diamond between the compact source and itself. The converse follows from the Green identities on compact distributions.

Displayed formulas in this passage

V-B@1#eq:compactprimitive · line 593
$E_{r} C = 0 ⟺ G_{r, A} C = G_{r, R} C =: A_{C} is compact, □ A_{C} = C .$

Nearby in this section

lemma: Lemma: Smooth propagation of the present sources
theorem: Theorem: Direct compact-current smoothing
section: Green identities and compact smoothing