前N个拉德马赫函数张成空间中L2范数的精确离散化
On exact discretization of the $L_2$-norm in the space spanned by the first $N$ Rademacher functions
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中文总结 AI 辅助
该研究探讨前N个拉德马赫函数张成空间中L2范数的精确离散化，得出最少节点数为N或N+1，且与阿达马矩阵及阿达马猜想存在关联。
中文摘要 AI 辅助
我们研究前N个拉德马赫函数张成空间中L2范数的精确离散化，证明节点数最少的离散化所需足够节点数为N或N+1，取决于维度N，还阐明其与阿达马矩阵及阿达马猜想的联系。
英文摘要
We study the exact discretization of the $L_2$-norm in the space spanned by the first $N$ Rademacher functions. It is shown that the sufficient number of nodes for discretization with the minimal number of nodes is equal to $N$ or $N+1$ and depends on the dimension $N$. The connection with Hadamard matrices and the Hadamard conjecture is demonstrated.
