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

Department of Mathematics

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

13 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
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 - 15 Nov 2016

Bibliographical note

Publisher Copyright:
© 2016 Elsevier Inc.

Funding

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

Funders	Funder number
Israel Science Foundation	225/13

Keywords

Fuglede's conjecture
Spectral set
Tiling

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10.1016/j.jfa.2016.04.021

Cite this

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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.

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KW - Tiling

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Spectrality and tiling by cylindric domains

Abstract

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Keywords

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