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.

引用

页码：1 / 6

页数：6

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