Spline wavelets in ℓ2(Z)

Compared with the spline wavelet decomposition for the discrete power growth space F given by Pevnyi and Zheludev, this paper deals with spline wavelet decompositions for the Hilbert space ℓ2(Z). We characterize RTB splines and RTB wavelets, because the space ℓ2(Z) can be represented by them. It turns out that the representation is stable and the convergence is much stronger than the pointwise convergence in F. Finally, a family of symmetric RTB wavelets with finite supports are constructed.