Manuscript XVIII-B@2 · XVIII-B-v2.tex · section · 27ed4f4b

Prepared response and its calculated residual

Prepared response and its calculated residual · lines 1323–1336

XVIII-B@2#eq:ramp

Fix a real smooth time ramp with

σ_{ε} (t) = 0 (t \leq 0), σ_{ε} (t) = 1 (t \geq ε), ε > 0.

It is not required to be a ultraviolet regulator. Take $h, j \in C_{c}^{\infty} (M; S^{2} T M)$ and $H = σ_{ε} h$ . Then $H$ is compact and smooth.

Displayed formulas in this passage

XVIII-B@2#eq:ramp · line 1327
$σ_{ε} (t) = 0 (t \leq 0), σ_{ε} (t) = 1 (t \geq ε), ε > 0.$