Manuscript En02-E@2 · En02-E-v2.tex · section · c2769986

A selected two-packet family

Analytical controls and numerical acceptance › A selected two-packet family · lines 1231–1249

On $B = [c - w /2, c + w /2] \subset (0, \infty)$ , choose

h_{1} = w^{- 1/2}, h_{2} = 12 w^{- 3/2} (ω - c),

zero outside $B$ . They are orthonormal and

H = (c w / 12 w / 12 c) .

The covariance $K$ is evaluated without deleting off-diagonal entries. Midpoint energy $c I$ has compressed error $w / 12$ , bounded by $w /2$ . These packets are not sharp arrival events.

Displayed formulas in this passage

unlabeled · line 1234
$h_{1} = w^{- 1/2}, h_{2} = 12 w^{- 3/2} (ω - c),$
unlabeled · line 1239
$H = (c w / 12 w / 12 c) .$

Nearby in this section

example: Example: Exact phase-sensitive algebraic control