e assume that the conditions
(
Compactly supported scaling
function
) and (
Sufficiently fine
scale
) hold and build on results of the previous section.
Notation
We introduce the notation
where the orthogonal complement is taken with respect to the
scalar
product.
The above is to be compared with the notation
(
Notation W_d
) and the proposition
(
Existence of orthonormal
wavelet bases 1
).
We proceed to construct an
orthogonal
basis for
.
It remains to perform orthogonalization of
similarly to the orthogonalization of
leading to
in the previous section.
