发表机构
Texas A&M University（德克萨斯农工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究gap-rich集合的识别，证明Zariski拓扑下局部稠密集合在非常数多项式下的像具有gap-rich性质，推广了先前工作，允许局部相关性和完全连通实现集合。
AI 中文摘要
gap-richness（间隙丰富性）的概念最近被引入，用于量化通过任意小扰动为周期词模型打开谱间隙的能力，并且在构造具有奇异谱性质的近周期算子中很有用，例如零Hausdorff维数的Cantor谱。给定欧几里得空间的一个在Zariski拓扑下局部稠密的子集，我们证明该集合在任何非常数多项式下的像都是gap-rich的。这在多个方面推广了先前工作的范围，包括允许局部相关性进入势块，并允许完全连通的实现集合。
英文摘要
The notion of gap-richness was recently introduced to quantify the ability to open spectral gaps for periodic word models by arbitrarily small perturbations and is useful in the construction of almost-periodic operators having exotic spectral properties, such as Cantor spectrum of zero Hausdorff dimension. Given a subset of Euclidean space that is locally dense in the Zariski topology, we show that any image of such a set under a nonconstant polynomial is gap-rich. This generalizes the scope of previous work in several ways, including allowing local correlations into potential blocks and allowing for totally disconnected sets of realizations.
Comments22 pages
