If we consider the B-splines's MRA of 0 and 1 orders, there is a relationship between the wavelets of one of them and the functions of the Riesz's basis of another. Besides, we have found a characterization for the two-scale sequences and Riesz's basis of these MRAs. Due to this new decomposition, the functions in Vj can be written using two expressions depending on the possible applications.
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