Manuscript XVI-K@1 · XVI-K.tex · section · aa7553bb

An operational action on jet-vanishing tests

A coherent extension map on the finite span › An operational action on jet-vanishing tests · lines 1195–1210

XVI-K@1#eq:operational

Choose any auxiliary cutoff $ζ \in C_{c}^{\infty} (R^{4})$ equal to one near zero. For $u \in H_{k}$ , $ρ = k - 4$ , define

T_{k, u} (ψ) = a ↓ 0 lim ⟨ u, (1 - ζ (\cdot / a)) ψ ⟩, ψ \in D_{ρ} .

Each test in the limit vanishes near zero, so its pairing uses only the punctured distribution.

Displayed formulas in this passage

XVI-K@1#eq:operational · line 1200
$T_{k, u} (ψ) = a ↓ 0 lim ⟨ u, (1 - ζ (\cdot / a)) ψ ⟩, ψ \in D_{ρ} .$