It is known [6], [14], [19] that if $\mathrm{\Omega }\subset {\mathbb{R}}^d$ belongs to a class of k-tiling domains when translated by a lattice Λ, there exists a Riesz basis of exponentials for $L^2(\mathrm{\Omega })$ constructed using k translates of the dual lattice ${\mathrm{\Lambda }}^{⁎}$. In this paper, we give an explicit construction of the corresponding biorthogonal dual Riesz basis. We also extend the iterative reconstruction algorithm introduced in [11] to this setting.

中文翻译：

---

在多平铺上寻找Riesz指数基础的对偶

众所周知[6]，[14]，[19] $\mathrm{\Omega }\subset {\mathbb{[R}}^d$当由晶格Λ转换时，属于k个平铺域的一类，存在一个Riesz基的指数${\mathrm{大号}}^2（\mathrm{\Omega }）$使用对偶晶格的k平移构造${\mathrm{\Lambda }}^{⁎}$。在本文中，我们给出了相应的双正交对偶Riesz基的显式构造。我们还将[11]中介绍的迭代重建算法扩展到该设置。