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Journal articles on the topic 'Fuglede conjecture'

Author: Grafiati

Published: 9 March 2023

Last updated: 31 July 2025

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1

DUTKAY, DORIN ERVIN, and CHUN–KIT LAI. "Some reductions of the spectral set conjecture to integers." Mathematical Proceedings of the Cambridge Philosophical Society 156, no. 1 (2013): 123–35. http://dx.doi.org/10.1017/s0305004113000558.

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AbstractThe spectral set conjecture, also known as the Fuglede conjecture, asserts that every bounded spectral set is a tile and vice versa. While this conjecture remains open on ${\mathbb R}^1$, there are many results in the literature that discuss the relations among various forms of the Fuglede conjecture on ${\mathbb Z}_n$, ${\mathbb Z}$ and ${\mathbb R}^1$ and also the seemingly stronger universal tiling (spectrum) conjectures on the respective groups. In this paper, we clarify the equivalences between these statements in dimension one. In addition, we show that if the Fuglede conjecture

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2

Lauric, Vasile. "Some consequences of quasicentral approximate units modulo Hilbert-Schmidt class." Mathematica Slovaca 69, no. 2 (2019): 433–36. http://dx.doi.org/10.1515/ms-2017-0235.

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Abstract Conjecture 4 of Voiculescu implies that almost normal operators must satisfy a Fuglede-Putnam theorem, namely [T∗, X] is a Hilbert-Schmidt operator whenever [T, X] is in the same class for an arbitrary operator X. In this note, a partial answer to this question is given, namely when X ∈ 𝓒4, the Fuglede-Putnam theorem holds.

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3

Iosevich, Alexander, Azita Mayeli та Jonathan Pakianathan. "The Fuglede conjecture holds in ℤp× ℤp". Analysis & PDE 10, № 4 (2017): 757–64. http://dx.doi.org/10.2140/apde.2017.10.757.

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4

Iosevich, Alex, Nets Katz, and Terence Tao. "The Fuglede spectral conjecture holds for convex planar domains." Mathematical Research Letters 10, no. 5 (2003): 559–69. http://dx.doi.org/10.4310/mrl.2003.v10.n5.a1.

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5

LYONS, RUSSELL. "Identities and Inequalities for Tree Entropy." Combinatorics, Probability and Computing 19, no. 2 (2009): 303–13. http://dx.doi.org/10.1017/s0963548309990605.

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The notion of tree entropy was introduced by the author as a normalized limit of the number of spanning trees in finite graphs, but is defined on random infinite rooted graphs. We give some new expressions for tree entropy; one uses Fuglede–Kadison determinants, while another uses effective resistance. We use the latter to prove that tree entropy respects stochastic domination. We also prove that tree entropy is non-negative in the unweighted case, a special case of which establishes Lück's Determinant Conjecture for Cayley-graph Laplacians. We use techniques from the theory of operators affil

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6

Kiss, Gergely, та Gábor Somlai. "Fuglede’s conjecture holds on ℤ_{𝕡}²×ℤ_{𝕢}". Proceedings of the American Mathematical Society 149, № 10 (2021): 4181–88. http://dx.doi.org/10.1090/proc/15541.

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The study of Fuglede’s conjecture on the direct product of elementary abelian groups was initiated by Iosevich et al. For the product of two elementary abelian groups the conjecture holds. For Z p 3 \mathbb {Z}_p^3 the problem is still open if p p is prime and p ≥ 11 p\ge 11 . In connection we prove that Fuglede’s conjecture holds on Z p 2 × Z q \mathbb {Z}_{p}^2\times \mathbb {Z}_q by developing a method based on ideas from discrete geometry.

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7

Bose, Debashish. "On Fuglede's conjecture for three intervals." Online Journal of Analytic Combinatorics, no. 5 (December 31, 2010): 1–24. https://doi.org/10.61091/ojac-505.

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In this paper, we prove the Tiling implies Spectral part of Fuglede’s cojecture for the three interval case. Then we prove the converse Spectral implies Tiling in the case of three equal intervals and also in the case where the intervals have lengths 1/2, 1/4, 1/4. Next, we consider a set Ω ⊂ R, which is a union of n intervals. If Ω is a spectral set, we prove a structure theorem for the spectrum provided the spectrum is assumed to be contained in some lattice. The method of this proof has some implications on the Spectral implies Tiling part of Fuglede’s conjecture for three intervals. In the

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8

Farkas, Bálint, and Révész Szilárd Gy. "Tiles with no spectra in dimension 4." MATHEMATICA SCANDINAVICA 98, no. 1 (2006): 44. http://dx.doi.org/10.7146/math.scand.a-14982.

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9

Matolcsi, Máté. "Fuglede’s conjecture fails in dimension 4." Proceedings of the American Mathematical Society 133, no. 10 (2005): 3021–26. http://dx.doi.org/10.1090/s0002-9939-05-07874-3.

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10

Greenfeld, Rachel, and Nir Lev. "Fuglede’s spectral set conjecture for convex polytopes." Analysis & PDE 10, no. 6 (2017): 1497–538. http://dx.doi.org/10.2140/apde.2017.10.1497.

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11

Fan, Aihua, Shilei Fan, Lingmin Liao, and Ruxi Shi. "Fuglede’s conjecture holds in $$\mathbb {Q}_{p}$$." Mathematische Annalen 375, no. 1-2 (2019): 315–41. http://dx.doi.org/10.1007/s00208-019-01867-8.

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12

Łaba, I. "Fuglede’s conjecture for a union of two intervals." Proceedings of the American Mathematical Society 129, no. 10 (2001): 2965–72. http://dx.doi.org/10.1090/s0002-9939-01-06035-x.

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13

Farkas, Balint, Mate Matolcsi, and Peter Mora. "On Fuglede's Conjecture and the Existence of Universal Spectra." Journal of Fourier Analysis and Applications 12, no. 5 (2006): 483–94. http://dx.doi.org/10.1007/s00041-005-5069-7.

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14

Tao, Terence. "Fuglede’s conjecture is false in 5 and higher dimensions." Mathematical Research Letters 11, no. 2 (2004): 251–58. http://dx.doi.org/10.4310/mrl.2004.v11.n2.a8.

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15

Greenfeld, Rachel, and Nir Lev. "Spectrality of product domains and Fuglede’s conjecture for convex polytopes." Journal d'Analyse Mathématique 140, no. 2 (2020): 409–41. http://dx.doi.org/10.1007/s11854-020-0092-9.

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16

Ferguson, Samuel J., and Nat Sothanaphan. "Fuglede’s conjecture fails in 4 dimensions over odd prime fields." Discrete Mathematics 343, no. 1 (2020): 111507. http://dx.doi.org/10.1016/j.disc.2019.04.026.

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17

An, Li-Xiang, Qian Li, and Min-Min Zhang. "The generalized Fuglede’s conjecture holds for a class of Cantor–Moran measures." Pacific Journal of Mathematics 334, no. 2 (2025): 189–209. https://doi.org/10.2140/pjm.2025.334.189.

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18

Zhang, Tao. "Fuglede’s Conjecture Holds in \(\boldsymbol{\mathbb{Z}_{p}\times \mathbb{Z}_{p^{n}}}\)." SIAM Journal on Discrete Mathematics 37, no. 2 (2023): 1180–97. http://dx.doi.org/10.1137/22m1493598.

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19

Mattheus, Sam. "A counterexample to Fuglede's conjecture in $(\mathbb{Z}/p\mathbb{Z})^4$ for all odd primes." Bulletin of the Belgian Mathematical Society - Simon Stevin 27, no. 4 (2020): 481–88. http://dx.doi.org/10.36045/j.bbms.190708.

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20

Kiss, Gergely, Romanos Diogenes Malikiosis, Gábor Somlai, and Máté Vizer. "Fuglede’s Conjecture Holds for Cyclic Groups of Order pqrs." Journal of Fourier Analysis and Applications 28, no. 5 (2022). http://dx.doi.org/10.1007/s00041-022-09972-0.

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AbstractThe tile-spectral direction of the discrete Fuglede-conjecture is well-known for cyclic groups of square-free order, initiated by Łaba and Meyerowitz, but the spectral-tile direction is far from being well-understood. The product of at most three primes as the order of the cyclic group was studied intensely in the last couple of years. In this paper we study the case when the order of the cyclic group is the product of four different primes and prove that Fuglede’s conjecture holds in this case.

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21

Birklbauer, Philipp. "The Fuglede Conjecture Holds in." Experimental Mathematics, July 12, 2019, 1–5. http://dx.doi.org/10.1080/10586458.2019.1636427.

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22

Zhou, Weiqi. "A Fuglede type conjecture for discrete Gabor bases." Banach Journal of Mathematical Analysis 18, no. 3 (2024). http://dx.doi.org/10.1007/s43037-024-00361-x.

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23

Fallon, Thomas, Azita Mayeli, and Dominick Villano. "The Fuglede conjecture holds in $(\mathbb {F}_p^3)$ for $(p=5,7)$." Proceedings of the American Mathematical Society, November 23, 2019, 1. http://dx.doi.org/10.1090/proc/14750.

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24

Dutkay, Dorin Ervin, and Palle E. T. Jorgensen. "The momentum operator on a union of intervals and the Fuglede conjecture." Sampling Theory, Signal Processing, and Data Analysis 21, no. 2 (2023). http://dx.doi.org/10.1007/s43670-023-00072-8.

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25

Malikiosis, Romanos Diogenes, and Mihail N. Kolountzakis. "Fuglede's conjecture on cyclic groups of order pnq." Discrete Analysis, September 5, 2018. http://dx.doi.org/10.19086/da.2071.

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26

Malikiosis, Romanos Diogenes. "A linear programming approach to Fuglede’s conjecture in $$\mathbb {Z}_p^3$$." Sampling Theory, Signal Processing, and Data Analysis 22, no. 1 (2023). http://dx.doi.org/10.1007/s43670-023-00078-2.

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AbstractWe present an approach to Fuglede’s conjecture in $$\mathbb {Z}_p^3$$ Z p 3 using linear programming bounds, obtaining the following partial result: if $$A\subseteq \mathbb {Z}_p^3$$ A ⊆ Z p 3 with $$p^2-p\sqrt{p}+\sqrt{p}<|A|<p^2$$ p 2 - p p + p < | A | < p 2 , then A is not spectral.

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27

Zhang, Tao. "A Group Ring Approach to Fuglede’s Conjecture in Cyclic Groups." Combinatorica, November 27, 2023. http://dx.doi.org/10.1007/s00493-023-00076-x.

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28

Chakraborty, Piyali, Dorin Ervin Dutkay, and Palle E. T. Jorgensen. "Fuglede’s conjecture, differential operators and unitary groups of local translations." Expositiones Mathematicae, February 2025, 125662. https://doi.org/10.1016/j.exmath.2025.125662.

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