论文标题
在离散周期运算符的光谱带上
On spectral bands of discrete periodic operators
论文作者
论文摘要
我们在$ \ mathbb z^d $上考虑离散的定期运算符，相对于lattices $γ\ subset \ subset \ mathbb z^d $的全等级。我们描述了晶格$γ$的类别，用于操作员可能会有频谱差距，以实现任意小电位的频谱差距。我们还表明，对于一大批晶格，频段边缘的光谱频段功能的级别集不超过$ d-2 $。
We consider discrete periodic operator on $\mathbb Z^d$ with respect to lattices $Γ\subset\mathbb Z^d$ of full rank. We describe the class of lattices $Γ$ for which the operator may have a spectral gap for arbitrarily small potentials. We also show that, for a large class of lattices, the dimensions of the level sets of spectral band functions at the band edges do not exceed $d-2$.
