Multi-tiling and Riesz bases

被引：43
|
作者：
Grepstad, Sigrid [1 ]
Lev, Nir [2 ,3 ]
机构：
[1] Norwegian Univ Sci & Technol NTNU, Dept Math Sci, NO-7491 Trondheim, Norway
[2] Ctr Recerca Matemat, Bellaterra 08193, Barcelona, Spain
[3] Bar Ilan Univ, Dept Math, IL-52900 Ramat Gan, Israel
来源：
ADVANCES IN MATHEMATICS | 2014年 / 252卷
基金：
以色列科学基金会;
关键词：
Riesz bases; Tiling; Quasicrystals; INTERPOLATING-SEQUENCES; QUASI-CRYSTALS; CONJECTURE; SETS;
D O I：
10.1016/j.aim.2013.10.019
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let S be a bounded, Riemann measurable set in R-d, and Lambda be a lattice. By a theorem of Fuglede, if S tiles R-d with translation set Lambda, then S has an orthogonal basis of exponentials. We show that, under the more general condition that S multi-tiles R-d with translation set Lambda, S has a Riesz basis of exponentials. The proof is based on Meyer's quasicrystals. (C) 2013 Elsevier Inc. All rights reserved.
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页码：1 / 6
页数：6
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