Construction of multivariate compactly supported prewavelets in L2 space and pre-Riesz bases in Sobolev spaces

We give a new constructive method for finding compactly supported prewavelets in L2 spaces in the multivariate setting. This method works for any dimensional space. When this method is generalized to the Sobolev space setting, it produces a pre-Riesz basis for Hs(Rd) which can be useful for applications.