论文标题
关于较低集和普遍离散的基数
On the cardinality of lower sets and universal discretization
论文作者
论文摘要
如果$（k_1，\ dots，k_d）\ in q $ in q $（l_1，l_1，\ dots，l_d）\ in q $ in q $ in $ \ mathbb {z} _+^d $ in q $ in q $ in q $ in q $ in q $ in $ \ mathbb {z} _+^d $是一个较低的集合。我们得出了有关$ \ Mathbb {z} _+^d $的较低尺寸$ n $的基数的新的和完善的结果。接下来，我们将这些结果应用于$ n $二维元素的元素元素的普遍离散化，该元素是由较低集合生成的三角多项式的。
A set $Q$ in $\mathbb{Z}_+^d$ is a lower set if $(k_1,\dots,k_d)\in Q$ implies $(l_1,\dots,l_d)\in Q$ whenever $0\le l_i\le k_i$ for all $i$. We derive new and refine known results regarding the cardinality of the lower sets of size $n$ in $\mathbb{Z}_+^d$. Next we apply these results for universal discretization of the $L_2$-norm of elements from $n$-dimensional subspaces of trigonometric polynomials generated by lower sets.
