Riesz bases of exponentials on unbounded multi-tiles
Riesz bases of exponentials on unbounded multi-tiles
复制标题
无界多重图块上的指数 Riesz 基
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
D. Carbajal
中科院分区：
文献类型：
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作者：
C. Cabrelli;D. Carbajal
我们证明了L^2(Omega)的指数Riesz基的存在性，只要R^d中的Omega是有限正测度的可测集，且满足多平铺条件和称为可容许性的算术性质.这一性质对任何有界域都是满足的，因此我们的结果推广了已知的有界多块的情况。我们还将关于次多瓦片和指数框架的已知结果推广到无界情形。
We prove the existence of Riesz bases of exponentials of L^2(Omega), provided that Omega in R^d is a measurable set of finite and positive measure, not necessarily bounded, that satisfies a multi-tiling condition and an arithmetic property that we call admissibility. This property is satisfied for any bounded domain, so our results extend the known case of bounded multi-tiles. We also extend known results for submulti-tiles and frames of exponentials to the unbounded case.