A simple condition for bounded displacement

Yaar Solomon

doi:10.1016/j.jmaa.2013.12.050

A simple condition for bounded displacement

Yaar Solomon

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

We study separated nets Y that arise from primitive substitution tilings of Rd. We show that the question whether Y is a bounded displacement of Zd or not can be reduced, in many cases, to a simple question on the eigenvalues and eigenspaces of the substitution matrix.

Original language	English
Pages (from-to)	134-148
Number of pages	15
Journal	Journal of Mathematical Analysis and Applications
Volume	414
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2013.12.050
State	Published - 1 Jun 2014
Externally published	Yes

Keywords

Separated nets
Substitution tiling

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2013.12.050

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title = "A simple condition for bounded displacement",

abstract = "We study separated nets Y that arise from primitive substitution tilings of Rd. We show that the question whether Y is a bounded displacement of Zd or not can be reduced, in many cases, to a simple question on the eigenvalues and eigenspaces of the substitution matrix.",

keywords = "Separated nets, Substitution tiling",

author = "Yaar Solomon",

note = "Funding Information: This research was supported by the Israel Science Foundation , grant 190/08 . I wish to thank my supervisor, Barak Weiss, for his many helpful remarks and ideas. I also wish to thank Eli Shamovich and Roi Livni for helpful conversations, and to the referee for his valuable remarks.",

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N1 - Funding Information: This research was supported by the Israel Science Foundation , grant 190/08 . I wish to thank my supervisor, Barak Weiss, for his many helpful remarks and ideas. I also wish to thank Eli Shamovich and Roi Livni for helpful conversations, and to the referee for his valuable remarks.

PY - 2014/6/1

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N2 - We study separated nets Y that arise from primitive substitution tilings of Rd. We show that the question whether Y is a bounded displacement of Zd or not can be reduced, in many cases, to a simple question on the eigenvalues and eigenspaces of the substitution matrix.

AB - We study separated nets Y that arise from primitive substitution tilings of Rd. We show that the question whether Y is a bounded displacement of Zd or not can be reduced, in many cases, to a simple question on the eigenvalues and eigenspaces of the substitution matrix.

KW - Separated nets

KW - Substitution tiling

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U2 - 10.1016/j.jmaa.2013.12.050

DO - 10.1016/j.jmaa.2013.12.050

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SP - 134

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JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

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ER -

A simple condition for bounded displacement

Abstract

Keywords

ASJC Scopus subject areas

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