e assume that
the conditions (
Biorthogonal
scaling functions
) and (
Sufficiently
fine scale 2
) hold and build on results of the previous section. We assume
that
and
.
We introduce the spaces
and
via the
relationships
The bases for
and
are constructed as follows.
Let
The space
has dimension
.
Hence, we construct a part of the basis for
by taking
and
.
The remaining
functions from
are derived by constructing the functions


(Wavelets on 01 step 1)

where
Similarly, on the right hand side of the interval
we construct the same
and
by
setting
We form the linear
combinations
for some finite sequences
,
,
,
determined below. The wavelet dual bases of the space
take the
form
The
,
,
,
are chosen to
satisfy
Let
for some matrixes
and
columns
Then
We conclude as in the previous
section:
