A proof of the gap labeling conjecture
A proof of the gap labeling conjecture
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间隙标记猜想的证明
DOI：
10.1307/mmj/1070919558
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发表时间：
2002
影响因子：
0.9
通讯作者：
I. Putnam
中科院分区：
文献类型：
--
作者：
J. Kaminker;I. Putnam
我们给出了J. Bellissard提出的差距标记猜想的证明。这提供了有关与准晶体相关的Schrodinger操作员的频谱的信息。该证明利用C. Moore和C. Schochet引入的Connes的索引定理的版本，适用于叶的空间。这些自然出现在动力学上，并且很可能有进一步的应用。
We give a proof of the Gap Labeling Conjecture formulated by J. Bellissard. This gives information about the spectrum of a Schrodinger operator associated to a quasicrystal. The proof makes use of a version of Connes' Index Theorem for Foliations which was introduced by C. Moore and C. Schochet and is appropriate for foliated spaces. These arise naturally in dynamics and are likely to have further applications.