roposition
(Sufficient conditions
for vanishing moments) Let
be an MRA, scaling function and wavelet (see the definition
(
Multiresolution analysis
) and
propositions (
Scaling
equation
),(
Existence
of orthonormal wavelet bases 2
)). Assume that
1.
is compactly supported and (therefore)
is finite, where the sequence
is defined in the proposition (
Scaling
equation
).
Then the following statements are equivalent:
(a)
,
,
for some
,
(b)
,
,
(c) there is a
representation
for some finite sequence
,
(d)
,
.
