Manuscript X-A-conv-ST@1 · X-A-conv-ST.tex · section · 8ca47088

The completion Cauchy operator

Stage B: Cauchy solution and regulator preflight › The completion Cauchy operator · lines 479–491

X-A-conv-ST@1#eq:Ezero

For a smooth source $s$ , define the zero-data inverse on $M_{8}$ :

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

The multiplier has its continuous value $t - u$ at zero spatial frequency.

Displayed formulas in this passage

X-A-conv-ST@1#eq:Ezero · line 482
$(E_{0} s) (t) = \int_{0}^{t} \frac{sin (( t - u ) - Δ )}{- Δ} s (u) d u .$