(Sufficient
conditions for vanishing moments 2) Let
and
be an pair of dual GMRAs, scaling functions and wavelets (see the definition
(
Dual wavelets
)). Assume that

1.
are compactly supported and (therefore)
are finite.

Then the following statements are equivalent:

(a)
,
,
for some
.

(b)
,
,

(c) there is a
representation
for some finite sequence
.