Relevant bibliographies by topics / Fuglede conjecture

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Academic literature on the topic 'Fuglede conjecture'

Author: Grafiati
Published: 9 March 2023
Last updated: 31 July 2025

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Journal articles on the topic "Fuglede conjecture"

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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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Fuglede conjecture"

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Shi, Ruxi. "Étude sur la conjecture de Fuglede et les suites oscillantes." Thesis, Amiens, 2018. http://www.theses.fr/2018AMIE0026/document.

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Dans cette thèse, nous résolvons la conjecture de Fuglede sur le corps des nombres p-adiques, et étudions certaines propriétés aléatoires des suites liées à la conjecture de Sarnak, ainsi que leur propriétés oscillantes. Dans la première partie, nous prouvons d'abord la conjecture de Fuglede pour des ensembles ouverts compacts dans Q_p. Celle-ci indique qu'un ensemble ouvert compact dans Q_p est un ensemble spectral si et seulement s'il pave Q_p par translation. Il est également prouvé qu'un ensemble ouvert compact est un ensemble spectral (ou une tuile) si et seulement s'il est p-homogène. No
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LANZAROTTO, GRETA. "EXTENDED VUZA CANONS." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2022. http://hdl.handle.net/10281/393094.

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In questa tesi ci occupiamo di Canoni Ritmici a Mosaico, che sono composizioni contrappuntistiche puramente ritmiche. I canoni nella musica hanno una tradizione molto lunga; tra questi emergono i canoni ritmici a mosaico (cioè, canoni tali che, dato un tempo, ad ogni battito suona esattamente una voce). Solo nel secolo scorso, a partire dall'analogo problema della fattorizzazione di gruppi abeliani finiti, sono stati studiati i canoni ritmici a mosaico aperiodici: si tratta di canoni che tassellano un certo intervallo di tempo in cui ciascuna voce (voce interna) suona su una sequenza aperiodic
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Conference papers on the topic "Fuglede conjecture"

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Siripuram, Aditya, and Brad Osgood. "LP relaxations and Fuglede's conjecture." In 2018 IEEE International Symposium on Information Theory (ISIT). IEEE, 2018. http://dx.doi.org/10.1109/isit.2018.8437309.

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Journal articles
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