Manuscript X-A-conv@1 · X-A-conv.tex · section · c76fffa3

The finite-time inverse

Cauchy operators and the regulated coordinate problem › The finite-time inverse · lines 824–838

X-A-conv@1#eq:Ezero

For a smooth source $s$ , define

(E_{0} s) (t) = \int_{0}^{t} \frac{sin (( t - u ) - Δ )}{- Δ} s (u) d u, 0 \leq t \leq 8.

The sine quotient has the continuous value $t - u$ at zero spatial frequency. Sources without decay are handled locally by finite propagation.

Displayed formulas in this passage

X-A-conv@1#eq:Ezero · line 827
$(E_{0} s) (t) = \int_{0}^{t} \frac{sin (( t - u ) - Δ )}{- Δ} s (u) d u, 0 \leq t \leq 8.$