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A method for constructing a new kind of spline basis functions ('2n(x)) with compact support on R was described by Ueno et al. (2007). These basis functions for sampling approximations consist of a linear combination of the cardinal B splines, but the construction is complicated and therefore were constructed basis functions '2n(x) only for n ≤ 5. We discuss a new construction of the basis functions and its approximation properties are considered.

A NEW METHOD FOR THE CONSTRUCTION OF SPLINE BASIS FUNCTIONS FOR SAMPLING APPROXIMATIONS