The operator that first truncates to a neighborhood of the origin in the spatial domain then truncates to a neighborhood of the origin in the spectral domain is investigated in the case of Boolean cubes. This operator is self adjoint on the space of functions spanned by the Laplacian eigenvectors corresponding to small eigenvalues. The eigenspaces of this iterated projection operator are studied through reduced matrices based on certain invariant subspaces. They are shown to depend fundamentally on the neighborhood structure of the cube defined in terms of Hamming distance.

中文翻译：

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布尔立方体的时空谱限制

在布尔立方体的情况下，首先研究在空间域中截断到原点附近，然后在频谱域中截断到原点附近的算子。该算子在与小特征值对应的拉普拉斯特征向量所跨越的函数空间上是自伴的。通过基于某些不变子空间的归约矩阵研究此迭代投影算子的本征空间。它们显示出基本上取决于根据汉明距离定义的立方体的邻域结构。