2.10 Let 0

????f(????) d???? < ∞, as in (2.83). Show that ????(0) − ????(h) =

O(|h|

????) as h → 0.

Hint: Write ????(0) − ????(h) = ∫ [1 − cos(hT????)] f(????) d???? in terms of the spectral density, and use the following inequalities:

(a) 1 − cos(x) ≤ 1 2

x2 for all x ≥ 0, so that?