Manuscript IX-D-ST@1 · IX-D-ST.tex · corollary · b1dc631a

Corollary: Support, including the spatial apex

Common-regulator evaluation · lines 1557–1576 · proof included or linked

IX-D-ST@1#cor:imagsupport, IX-D-ST@1#eq:imagsupport

In the open positive-time chart,

supp Im K = {(x, y) : ∣ t - s ∣ \leq ∣ x - y ∣ \leq t + s} .

Proof. For $R > 0$ , (eq:imag) vanishes off the displayed closed slab and is positive and smooth in its interior. Every point of the slab with $R > 0$ is a limit of interior points. At $R = 0$ , the slab requires $t = s$ . Those points are also limits of interior points. Lemma lem:radial supplies the global distributions and introduces no support outside the closure.

Displayed formulas in this passage

IX-D-ST@1#eq:imagsupport · line 1560
$supp Im K = {(x, y) : ∣ t - s ∣ \leq ∣ x - y ∣ \leq t + s} .$

Nearby in this section

section: Common-regulator evaluation
lemma: Lemma: Fourier existence
section: Common-regulator evaluation
proposition: Proposition: Exact direct-plus-reflected subtraction
lemma: Lemma: Global radial representatives
theorem: Theorem: Exact imaginary part
section: Common-regulator evaluation
section: Common-regulator evaluation