On the interpolation by discrete splines with equidistant nodes. (English) Zbl 0941.41002

In this paper the authors develop the theory of non-periodic discrete splines of power growth. Such splines are relevant for the purposes of digital signal processing. Discrete \(B\)-splines are introduced as linear combinations of shifts of the \(B\)-splines. Here the authors present a solution of the problem of discrete spline cardinal interpolation of the sequences of power growth and prove that the solution is unique within the class of discrete splines of a given order.


41A05 Interpolation in approximation theory
41A15 Spline approximation
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