Manuscript XV-B@2 · XV-B.tex · proposition · 4d3f12e8

Proposition: A local insertion wavefront upper bound

Supported extension, ambiguity, and closed-set estimates › Insertion wavefront bounds do not become output bounds · lines 1202–1224 · proof included or linked

XV-B@2#prop:insertWF, XV-B@2#eq:insertWF

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For $b \in D^{'} (X)$ ,

WF (E_{γ} b) \subset {(x, 0; ξ, η) : (x, ξ) \in WF (b) \cup (supp b \times {0}), η \in R^{m}, (ξ, η) \neq = 0} .

Proof. The insertion is $b \otimes \partial_{q}^{γ} δ_{0}$ . The tensor-product wavefront bound, with zero covectors adjoined on the supports of the factors, gives (eq:insertWF). Differentiation does not enlarge that bound Hormander (Section 8.2).

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XV-B@2#eq:insertWF · line 1205
$WF (E_{γ} b) \subset {(x, 0; ξ, η) : (x, ξ) \in WF (b) \cup (supp b \times {0}), η \in R^{m}, (ξ, η) \neq = 0} .$

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section: Insertion wavefront bounds do not become output bounds