Construction of orthogonal compactly-supported scaling functions and multiwavelets on arbitrary meshes

This paper will generalize the construction of a class of orthogonal, compactly-supported scaling vectors on 1-dimensional and 2-dimensional domains. A general procedure will be developed in both settings for the explicit construction of the associated multiwavelets on a uniform mesh, that is, a partition in R or a triangulation in R{dollar}sp2{dollar}.; The class of scaling functions presented in this paper are easily adapted to an arbitrary mesh. The methods for constructing the associated multiwavelets on a uniform mesh are generalized to arbitrary meshes. Examples and illustrations are provided.