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.

翻译：我们在周期指数B样条生成的平移不变空间中推导了带导数采样的充分条件。这些充分条件通过一种衡量连续采样点间距的新概念来表达。这些条件接近最优，尤其表明存在下Beurling密度任意接近必要密度的采样集。