Fuglede's conjecture for a union of two intervals
Classical Analysis and ODEs
2007-05-23 v1
Authors:
I. Laba
Abstract
We prove that a union of two intervals in R is a spectral set if and only if it tiles R by translations.
Cite
@article{arxiv.math/0002067,
title = {Fuglede's conjecture for a union of two intervals},
author = {I. Laba},
journal= {arXiv preprint arXiv:math/0002067},
year = {2007}
}
Comments
9 pages
Related papers
View all related →
Classical Analysis and ODEs · Mathematics
On Fuglede's conjecture for three intervals
Debashish Bose, C. P. Anil Kumar, R. Krishnan, Shobha Madan
2010-02-23
Classical Analysis and ODEs · Mathematics
"Spectral implies Tiling" for Three Intervals Revisited
Debashish Bose, Shobha Madan
2011-07-27
Classical Analysis and ODEs · Mathematics
Fuglede's conjecture holds in $\mathbb{Q}_p$
Aihua Fan, Shilei Fan, Lingmin Liao, Ruxi Shi
2015-12-31
Functional Analysis · Mathematics
On the universal tiling conjecture in dimension one
Dorin Ervin Dutkay, Palle E. T. Jorgensen
2013-01-25
Classical Analysis and ODEs · Mathematics
The Fuglede Conjecture holds in ${\Bbb Z}_p \times {\Bbb Z}_p$
Alex Iosevich, Azita Mayeli, Jonathan Pakianathan
2017-06-14
Classical Analysis and ODEs · Mathematics
Spectrality of product domains and Fuglede's conjecture for convex polytopes
Rachel Greenfeld, Nir Lev
2018-07-03
Classical Analysis and ODEs · Mathematics
Fuglede's spectral set conjecture for convex polytopes
Rachel Greenfeld, Nir Lev
2018-03-16
Classical Analysis and ODEs · Mathematics
The Fuglede conjecture holds in $\mathbb{Z}^3_5$
Philipp Birklbauer
2019-02-07
Functional Analysis · Mathematics
Some reductions of the spectral set conjecture to integers
Dorin Ervin Dutkay, Chun-Kit Lai
2014-01-14
Combinatorics · Mathematics
A group ring approach to Fuglede's conjecture in cyclic groups
Tao Zhang
2022-11-01
Classical Analysis and ODEs · Mathematics
The Fuglede Conjecture holds in \(\F_p^3\) for p=5,7
Thomas Fallon, Azita Mayeli, Dominick Villano
2019-06-11
Classical Analysis and ODEs · Mathematics
The Fuglede conjecture for convex domains is true in all dimensions
Nir Lev, Máté Matolcsi
2022-07-05
Number Theory · Mathematics
Spectra of certain types of polynomials and tiling of integers with translates of finite sets
Sergei Konyagin, Izabella Laba
2007-05-23
Classical Analysis and ODEs · Mathematics
Fuglede's conjecture holds on cyclic groups $\mathbb{Z}_{pqr}$
Ruxi Shi
2019-10-15
Classical Analysis and ODEs · Mathematics
Tiling sets and spectral sets over finite fields
C. Aten, B. Ayachi, E. Bau, D. FitzPatrick +13
2015-09-04
Classical Analysis and ODEs · Mathematics
Tiling, spectrality and aperiodicity of connected sets
Rachel Greenfeld, Mihail N. Kolountzakis
2024-11-14
Classical Analysis and ODEs · Mathematics
Spectral sets in $\mathbb{Z}_{p^2qr}$ tile
Gábor Somlai
2023-05-26
Classical Analysis and ODEs · Mathematics
Tiling the field $\mathbb{Q}_p$ of $p$-adic numbers by a function
Shilei Fan
2025-01-15
Classical Analysis and ODEs · Mathematics
Spectrum is periodic for n-Intervals
Debashish Bose, Shobha Madan
2010-04-13
Functional Analysis · Mathematics
Unitary groups and spectral sets
Dorin Ervin Dutkay, Palle E. T. Jorgensen
2014-11-06
Classical Analysis and ODEs · Mathematics
Spectrality and tiling by cylindric domains
Rachel Greenfeld, Nir Lev
2016-09-26
Functional Analysis · Mathematics
Some Plancherel identities for unbounded subsets of $\mathbb R$ in duality
Piyali Chakraborty, Dorin Ervin Dutkay
2026-03-05
Classical Analysis and ODEs · Mathematics
Spectral sets and weak tiling
Mihail N. Kolountzakis, Nir Lev, Máté Matolcsi
2023-10-24
Functional Analysis · Mathematics
Spectral properties of unions of intervals and groups of local translations
Bryan Ducasse, Dorin Ervin Dutkay, Colby Fernandez
2025-06-24
Functional Analysis · Mathematics
Universal Spectra and Tijdeman's Conjecture on Factorization of Cyclic Groups
Jeffrey C. Lagarias, Sandor Szabo
2007-05-23