Direct Paths of Wavelets
 Citation data:

The Houston Journal of Mathematics, University of Houston
 Publication Year:
 2003

 Bepress 4
 Repository URL:
 http://csuepress.columbusstate.edu/bibliography_faculty/328
 Author(s):
 Tags:
 Mathematics
article description
We associate a von Neumann algebra with each pair of complete wandering vectors for a unitary system. When this algebra is nonatomic, there is a normâ€“continuous path of a simple nature connecting the original pair of wandering vectors. We apply this technique to wavelet theory and compute the above von Neumann algebra in some special cases. Results from selection theory and ergodic theory lead to nontrivial examples where both atomic and nonatomic von Neumann algebras occur.