On Non-Periodic Tilings of the Real Line by a Function

被引：7
|
作者：
Kolountzakis, Mihail N. [1 ]
Lev, Nir [2 ]
机构：
[1] Univ Crete, Dept Math & Appl Math, Voutes Campus, GR-70013 Iraklion, Crete, Greece
[2] Bar Ilan Univ, Dept Math, IL-52900 Ramat Gan, Israel
来源：
INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2016年 / 2016卷 / 15期
基金：
以色列科学基金会;
关键词：
D O I：
10.1093/imrn/rnv283
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
It is known that a positive, compactly supported function f is an element of L-1(R) can tile by translations only if the translation set is a finite union of periodic sets. We prove that this is not the case if f is allowed to have unbounded support. On the other hand, we also show that if the translation set has finite local complexity, then it must be periodic, even if the support of f is unbounded.
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页码：4588 / 4601
页数：14
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