For the Hardy classes of functions analytic in the strip around real axis of a size 2β, an optimal method of cardinal interpolation has been proposed within the framework of Optimal Recovery [12]. Below this method, based on the Jacobi elliptic functions, is shown to be optimal according to the criteria of Nonparametric Regression and Optimal Design.In a stochastic non-asymptotic setting, the maximal mean squared error of the optimal interpolant is evaluated explicitly, for all noise levels away from 0. A pivotal role is played by the interference effect, in which the oscillations exhibited by the interpolant’s bias and variance mutually cancel each other. In the limiting case β → ∞, the optimal interpolant converges to the well-knownNyquist–Shannon cardinal series.

中文翻译：

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关于最佳基数插值

对于分析围绕2β大小的实轴的条带中的Hardy类函数，已在“最佳恢复”框架内提出了一种基数插值的最佳方法[12]。在下面的方法中，根据Jacobi椭圆函数，根据非参数回归和最优设计准则证明是最优的。在随机非渐近设置中，显式评估了最优插值的最大均方误差噪声水平远离0。干扰效应起着关键作用，其中插值器的偏差和方差表现出的振荡相互抵消。在极限→ β →∞的情况下，最优插值收敛于著名的奈奎斯特–香农基数级数。