Spline Wavelets 1 Theory and Algorithms for Non-Uniform Spline Wavelets

We investigate mutually orthogonal spline wavelet spaces on non-uniform partitions of a bounded interval, addressing the existence, uniqueness and construction of bases of minimally supported spline wavelets. The relevant algorithms for decompo- sition and reconstruction are considered as well as some stability-related questions. In addition, we briefly review the bivariate case for tensor products and arbitrary triangu- lations. We conclude the paper with a discussion of some special cases.