Nested spline--wavelet decompositions (Q690798)

The authors study embedded spline spaces (in general, non-smooth and non-polynomial) and the related spline-wavelet decompositions. The embedded spaces are obtained by removing simultaneously a group of grid points (nest), technique motivated by the case when delays in the processing of incoming numerical flows are possible. The related nested spline-wavelet decomposition is presented, together with the matrices of embedding and extension and with formula for decomposition and reconstruction. The decomposition and reconstruction operators are studied in spaces of finite sequences and also the technique to extend the results from one nest to a finite set of nests is presented.