Nonsmooth spline-wavelet expansions and their properties (Q690602)

The authors proposes some methods of constructing embedded spaces of splines and their wavelet expansions. Embedded spaces of nonsmooth splines of the first order and irregular meshes are considered. For a less finer mesh, the conditions under which the spline space is embedded into a similar space on the original mesh are discussed. Wavelet expansions are presented and it is shown that the expansions based on coarser meshes obtained by successively the removing mesh nodes are independent of the order in which nodes are removed; hence the decomposition operators are commutative.