Manuscript VII-B@1 · VII-B.tex · proposition · be632835

Proposition

Two precise repairs and their limitations › Refusal of an exact smooth off-shell replacement · lines 1278–1292 · proof included or linked

VII-B@1#prop:no-smooth-offshell

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If $q_{a}$ is singular, there is no smooth compactly supported tensor $s$ such that

⟨ q_{a}, h ⟩ = ⟨ s, h ⟩

for every smooth $h$ .

Proof. The equality would in particular hold for all compactly supported smooth $h$ , and hence would imply $q_{a} = s$ as distributions, contradicting singularity.

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unlabeled · line 1282
$⟨ q_{a}, h ⟩ = ⟨ s, h ⟩$

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section: Refusal of an exact smooth off-shell replacement