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arXiv · 2608.25058

On exact discretization of the $L_2$-norm in the space spanned by the first $N$ Rademacher functions

Anna Kazakova
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Abstract

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.

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Anna Kazakova. 2026-08-25. On exact discretization of the $L_2$-norm in the space spanned by the first $N$ Rademacher functions. https://arxiv.org/abs/2608.25058

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