Abstract
Using the decomposition method, we present in this paper constructions of multiresolution analyses on a compact Riemannian manifold
M of dimension
n
(
n
∈
N
)
. These analyses are generated by a finite number of basic functions and are adapted to the study of the Sobolev spaces
H
1
(
M
)
and
H
0
1
(
M
)
.