Manuscript VII-H@1 · VII-H.tex · example · d20d2a9f

Example: An elementary zero-data memory term

Why the same shortcuts fail in a more general response › Late source agreement does not erase preparation memory · lines 1568–1579

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Choose $F \in C_{c}^{\infty} ((0, ε))$ , $F \geq 0$ , $F \neq \equiv 0$ . The sources $F$ and zero agree for $t \geq ε$ , but their zero-data response difference is

z (t) = \int_{0}^{t} (t - s) F (s) d s .

For $t \geq ε$ ,

z (t) = t \int F - \int s F > 0.

Displayed formulas in this passage

unlabeled · line 1572
$z (t) = \int_{0}^{t} (t - s) F (s) d s .$
unlabeled · line 1576
$z (t) = t \int F - \int s F > 0.$

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section: Late source agreement does not erase preparation memory