Minimal Properties of Periodic Box-Spline Interpolation on a Three Direction Mesh

Abstract

Let ø be a piecewise continuous complex valued function on ℝ^s, s ≥ 1, which is 2π-periodic in each coordinate direction. Given a “meshsize” h = 2π/N, N ≥ 1, let F := F _h := h Z ^s ∩ [0, 2π)^s and

$$S():={{S}_{h}}():=\left\{ \sum\limits_{j\in \text{F}}{{{a}_{j}}(.-j)\left| {{a}_{j}}\in \mathbb{C} \right.} \right\}$$

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