n this section we start construction
of a piecewise linear MRA.
Let


(V for linear MRA 0)

We satisfy the requirement
(
Multiresolution analysis
)4 by
taking


(V for linear MRA d)

The requirement (
Multiresolution
analysis
)3 is satisfied because
is allowed to approach
.
Hence, we must have
and linearity on
and
for any
.
Thus,
for any such
.
The requirement (
Multiresolution
analysis
)2 is satisfied because one can
approximate
a
function with a sequence of linear functions on
for growing
.
The requirement (
Multiresolution
analysis
)1 is trivial.
The requirement (
Multiresolution
analysis
)5 is the key nontrivial component. It requires some preliminary
development.
