Manuscript Em01-F@3 · Em01-F-v3.tex · section · 225e59af

Tests

Tensor conventions and separated characteristic geometry › Tests · lines 487–502

Write $w = (a, b, z, y)$ . The label $J$ is dual to the marked tensor input of Section sec:insertion. For $U ⋐ M^{4}$ , set

T = D (U; S^{*}), ∥Φ ∥_{m, L} = J, ∣ γ ∣ \leq m max U sup ∣ \partial^{γ} Φ_{J} ∣, supp Φ \subset L ⋐ U .

Strong distributional convergence is uniform convergence on bounded test sets. Such sets have common compact support and bounded derivative seminorms of every order.

Displayed formulas in this passage

unlabeled · line 492
$T = D (U; S^{*}), ∥Φ ∥_{m, L} = J, ∣ γ ∣ \leq m max U sup ∣ \partial^{γ} Φ_{J} ∣, supp Φ \subset L ⋐ U .$