Manuscript XV-F-patch-ii@1 · XV-F-patch-ii.tex · corollary · 9674ac67

Corollary: Conditional smoothness of F

Patch 3: coefficient instantiation (Q3) › The response fiber map, b , g , and the advanced operator · lines 1292–1302 · proof included or linked

XV-F-patch-ii@1#cor:compact

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If $f \in C^{\infty}_{c} (R^{4})$ and $E^{A}_{m}$ is the kernel of Lemma lem:advanced, then $F = E^{A}_{m} * f \in C^{\infty}$ , the hypothesis $F \in C^{\infty}$ of (P1) is satisfied, and $K_{9}$ has $b$ -support in $supp g \cap (supp f + J^{-})$ .

Proof. Lemma lem:advanced and the factor $g (b) F (b)$ in (eq:K9).

Nearby in this section

section: The response fiber map, b , g , and the advanced operator
lemma: Lemma: The advanced kernel, conditionally
section: The response fiber map, b , g , and the advanced operator