标题： 带有导数的采样定理，在由周期指数B样条生成的平移不变空间中 显示英文标题

标题： Sampling theorems with derivatives in shift-invariant spaces generated by periodic exponential B-splines

摘要： 我们推导了在由周期性指数B样条生成的平移不变空间中使用导数进行采样的充分条件。 这些充分条件通过一种新的测量连续样本之间间隔的概念来表达。 这些条件接近最优，并且特别地，它们表明存在采样集，其下Beurling密度可以任意接近必要的密度。 显示英文摘要

摘要： We derive sufficient conditions for sampling with derivatives in shift-invariant spaces generated by a periodic exponential B-spline. The sufficient conditions are expressed with a new notion of measuring the gap between consecutive samples. These conditions are near optimal, and, in particular, they imply the existence of sampling sets with lower Beurling density arbitrarily close to the necessary density.