This paper considers the Fourier transform over the slice of the Boolean hypercube. We prove a relationship between the Fourier coefficients of a function over the slice, and the Fourier coefficients of its restrictions. As an application, we prove a Goldreich-Levin theorem for functions on the slice based on the Kushilevitz-Mansour algorithm for the Boolean hypercube.

翻译：本文审视了Fourier在布林超立方体切片上的变异。 我们证明了福里埃在切片上的函数系数与限制的福里埃系数之间的关系。 作为应用,我们证明了Goldreich-Levin对基于库希列维茨-曼苏尔计算法的博利安超立方体的切片功能的理论。