谱与Tilings关系中的测度估计和平移对

李建林, 闫莉, 姚海洪

数学学报 ›› 2012, Vol. 55 ›› Issue (3) : 449-456.

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数学学报 ›› 2012, Vol. 55 ›› Issue (3) : 449-456. DOI: 10.12386/A2012sxxb0042
论文

谱与Tilings关系中的测度估计和平移对

    李建林, 闫莉, 姚海洪
作者信息 +

Measure Estimates and Translative Pairs in the Spectra-Tilings Relations

    Jian Lin LI, Li YAN, Hai Hong YAO
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文章历史 +

摘要

本文将在两种特有的情形下研究谱与tilings之间的关系. 首先,估计和比较谱与tilings关系中集合的Lebesgue测度,这包括一些不能直接用密度方法所得结果的推广,以及在正交对、填充对与覆盖对中集合的Lebesgue测度的比较. 其次,明确了平移对(D,Λ+Γ)与(D+Λ,Γ)之间的一些谱与tilings关系.这里的研究是基于谱与tilings的基本性质, 与共轭Fuglede猜想密切相关.

Abstract

In the present paper we will study the relations between spectra and tilings in two special cases. We first estimate and compare the Lebesgue measure of sets in the spectra-tilings relations. This includes a generalization of several results when the density method fails to apply, and the comparison of Lebesgue measure of sets among the orthogonal pairs, packing pairs and covering pairs. We then clarify some spectratilings relations between the translative pairs (D,Λ+Γ) and (D+Λ,Γ). The research here is based on the fundamental properties of spectra and tilings, and is closely related to the dual Fuglede conjecture.

关键词

谱对 / 填充与覆盖 / tiling对

Key words

spectral pair / packing and covering / tiling pair

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李建林, 闫莉, 姚海洪. 谱与Tilings关系中的测度估计和平移对. 数学学报, 2012, 55(3): 449-456 https://doi.org/10.12386/A2012sxxb0042
Jian Lin LI, Li YAN, Hai Hong YAO. Measure Estimates and Translative Pairs in the Spectra-Tilings Relations. Acta Mathematica Sinica, Chinese Series, 2012, 55(3): 449-456 https://doi.org/10.12386/A2012sxxb0042

参考文献

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基金

国家自然科学基金资助项目(10871123,11171201);陕西省自然科学基金资助项目(2011JM1007)
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