On spectral bands of discrete periodic operators

Nikolay Filonov; Ilya Kachkovskiy

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arXiv · 2205.10496

On spectral bands of discrete periodic operators

Nikolay Filonov·Ilya Kachkovskiy

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Abstract

We consider discrete periodic operator on $\mathbb Z^d$ with respect to lattices $\Gamma\subset\mathbb Z^d$ of full rank. We describe the class of lattices $\Gamma$ 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 $d-2$.

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BibTeX RIS

Nikolay Filonov, Ilya Kachkovskiy. 2022-05-21. On spectral bands of discrete periodic operators. https://arxiv.org/abs/2205.10496

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