Spectrality and tiling by cylindric domains

Rachel Greenfeld; Nir Lev

doi:10.1016/j.jfa.2016.04.021

Spectrality and tiling by cylindric domains

Rachel Greenfeld, Nir Lev^*

^*Corresponding author for this work

Mathematics

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

9 Scopus citations

Abstract

A bounded set Ω⊂R^d is called a spectral set if the space L²(Ω) admits a complete orthogonal system of exponential functions. We prove that a cylindric set Ω is spectral if and only if its base is a spectral set. A similar characterization is obtained of the cylindric sets which can tile the space by translations.

Original language	English (US)
Pages (from-to)	2808-2821
Number of pages	14
Journal	Journal of Functional Analysis
Volume	271
Issue number	10
DOIs	https://doi.org/10.1016/j.jfa.2016.04.021
State	Published - Nov 15 2016

Funding

Research partially supported by the Israel Science Foundation grant No. 225/13 .

Keywords

Fuglede's conjecture
Spectral set
Tiling

ASJC Scopus subject areas

Analysis

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10.1016/j.jfa.2016.04.021

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title = "Spectrality and tiling by cylindric domains",

abstract = "A bounded set Ω⊂Rd is called a spectral set if the space L2(Ω) admits a complete orthogonal system of exponential functions. We prove that a cylindric set Ω is spectral if and only if its base is a spectral set. A similar characterization is obtained of the cylindric sets which can tile the space by translations.",

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author = "Rachel Greenfeld and Nir Lev",

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T1 - Spectrality and tiling by cylindric domains

AU - Greenfeld, Rachel

AU - Lev, Nir

PY - 2016/11/15

Y1 - 2016/11/15

N2 - A bounded set Ω⊂Rd is called a spectral set if the space L2(Ω) admits a complete orthogonal system of exponential functions. We prove that a cylindric set Ω is spectral if and only if its base is a spectral set. A similar characterization is obtained of the cylindric sets which can tile the space by translations.

AB - A bounded set Ω⊂Rd is called a spectral set if the space L2(Ω) admits a complete orthogonal system of exponential functions. We prove that a cylindric set Ω is spectral if and only if its base is a spectral set. A similar characterization is obtained of the cylindric sets which can tile the space by translations.

KW - Fuglede's conjecture

KW - Spectral set

KW - Tiling

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M3 - Article

AN - SCOPUS:84964871202

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EP - 2821

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 10

ER -

Spectrality and tiling by cylindric domains

Abstract

Funding

Keywords

ASJC Scopus subject areas

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