检测傅立叶子空间
Detecting Fourier subspaces
摘要：
设G是有限阿贝尔群.我们研究了l^2（G）在标准基上对角化的子空间和在对偶傅立叶基上对角化的子空间之间的差异。一般的原理是，与|G| = dim（l ^2（G））相比维数较小的傅立叶子空间往往远离标准子空间。特别是，最近的正解的Kadison-Singer问题表明，从任何傅立叶子空间，其尺寸是小的相比，|G|有标准的子空间，这是本质上是不可区分的，从它的正交补。
英文摘要：
Let G be a finite abelian group. We examine the discrepancy between subspaces of l^2(G) which are diagonalized in the standard basis and subspaces which are diagonalized in the dual Fourier basis. The general principle is that a Fourier subspace whose dimension is small compared to |G| = dim(l^2(G)) tends to be far away from standard subspaces. In particular, the recent positive solution of the Kadison-Singer problem shows that from within any Fourier subspace whose dimension is small compared to |G| there is standard subspace which is essentially indistinguishable from its orthogonal complement.
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