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On the ℓ4:ℓ2 ratio of functions with restricted Fourier support
Journal of Combinatorial Theory Series A ( IF 1.1 ) Pub Date : 2020-01-14 , DOI: 10.1016/j.jcta.2019.105202 Naomi Kirshner , Alex Samorodnitsky
中文翻译:
在ℓ 4:ℓ 2与限制傅立叶支持比率的函数
更新日期:2020-01-14
Journal of Combinatorial Theory Series A ( IF 1.1 ) Pub Date : 2020-01-14 , DOI: 10.1016/j.jcta.2019.105202 Naomi Kirshner , Alex Samorodnitsky
Given a subset , let be the maximal ratio between and norms of a function whose Fourier support is a subset of A.1 We make some simple observations about the connections between and the additive properties of A on one hand, and between and the uncertainty principle for A on the other hand. One application obtained by combining these observations with results in additive number theory is a stability result for the uncertainty principle on the discrete cube.
Our more technical contribution is determining rather precisely, when A is a Hamming sphere for all .
中文翻译:
在ℓ 4:ℓ 2与限制傅立叶支持比率的函数
给定一个子集 ,让 是之间的最大比例 和 其Fourier支持是A的子集的函数的范数。1我们对之间的联系进行了一些简单的观察一方面与A的可加性另一方面,A的不确定性原理。通过将这些观察结果与加法数论的结果相结合而获得的一个应用是离散立方体上不确定性原理的稳定性结果。
我们更多的技术贡献是确定 确切地说,当A是汉明球时 对全部 。