论文标题
关于通用抽样表示
On universal sampling representation
论文作者
论文摘要
对于多元三角多项式，我们从离散化的角度研究了de la vallee poussin内核的卷积。换句话说，我们以这种方式替换了归一化的Lebesgue度量，从而保留了卷积属性并提供了积分规范的抽样离散化。我们证明，在两种变化的情况下，斐波那契点集提供了理想的解决方案。我们还表明，Korobov点集为任意数量的变量提供了次优的（超过对数因素）解决方案。
For the multivariate trigonometric polynomials we study convolution with the corresponding the de la Vallee Poussin kernel from the point of view of discretization. In other words, we replace the normalized Lebesgue measure by a discrete measure in such a way, which preserves the convolution properties and provides sampling discretization of integral norms. We prove that in the two-variate case the Fibonacci point sets provide an ideal (in the sense of order) solution. We also show that the Korobov point sets provide a suboptimal (up to logarithmic factors) solution for an arbitrary number of variables.
