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Fuglede's conjecture holds in q p

WebOct 27, 2006 · Fuglede’s conjecture and the Universal Spectrum Conjecture remains open in 1 and 2 dimensions. The one-dimensional case is closely related to a number … WebFuglede's conjecture in Q_p is proved. That is to say, a Borel set of positive and finite Haar measure in Q_p is a spectral set if and only if it tiles Q_p by translation. arXiv:1512.08904v1 fatcat:wqxrs3uupjeapcpwqc5zp2lvgy

Fuglede’s conjecture holds on Z2 Zq - users.renyi.hu

WebJul 12, 2024 · Recently Iosevich, Mayeli and Pakianathan showed that the Fuglede conjecture holds over prime fields when the dimension does not exceed 2. The question for dimension 3 was previously addressed by Aten et al. for p = 3. In this paper we build upon those results by Aten et al. to allow a computer to carry out the lengthy computations. WebSep 5, 2024 · Editorial introduction. Fuglede’s conjecture on cyclic groups of order p n q, Discrete Analysis 2024:12, 16 pp. A conjecture of Fuglede from 1974 states that a measurable set E ⊂ R n of positive Lebesgue measure tiles R n by translations if and only if the space L 2 ( E) admits an orthonormal basis of exponential functions { e 2 π i λ ⋅ ... horse racing naps of the day https://thecircuit-collective.com

Equi‐distributed property and spectral set conjecture on Zp2×Zp

WebDec 15, 2024 · Abstract: 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 … WebP.O. Box 1160 Lexington,VA 24450 Rockingham Rockingham County Tax Assessor Barb Lowell 540-564-3067 540-654-1488 20 East Gay Street Harrisonburg, VA 22802 Russell Russell County Tax Assessor Eliza Williams 276-889-8018 276-889-8212 137 Highlands Drive Lebanon, VA 24266 Alphabetical listing of Virginia County Tax Assessors WebWelcome to Virginia Assessors! Virginia Assessors is your doorway to all Virginia County websites for on-line Parcel, Tax & GIS Data. Search parcel data, tax digest & GIS maps by Owners Name, Location Address, Parcel Number, Legal Description, or Account Number. You may also search by Map, Sales List or perform complicated Sales Searches to … horse racing names triple crown

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Category:Fuglede’s conjecture holds in \(\mathbb {Q}_{p}\) - Springer

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Fuglede's conjecture holds in q p

On Fuglede

WebX. Fuglede’s conjecture on Q p Theorem (A. Fan, S. Fan, L, R. Shi, J. Funct. Anal. 2016) A Borel set 2Qpis a spectral set if and only if it tiles Qp. ... analmost compact open set,if 9compact open 00ˆQpsuch that m(n 0) = m(n) = 0: Lingmin LIAO University Paris-East Cr eteil Fuglede’s conjecture holds in the eld of p-adic numbers 19/32. WebDec 30, 2015 · Abstract. Fuglede's conjecture in $\mathbb {Q}_p$ is proved. That is to say, a Borel set of positive and finite Haar measure in …

Fuglede's conjecture holds in q p

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WebFeb 8, 2024 · For p=5,7, we show that a subset \(E \subset \F_p^3\) is spectral if and only if E tiles \(\F_p^3\) by translation. Additionally, we give an alternate proof that the … WebAbstract. We show that the spectral set conjecture by Fuglede holds in the setting of cyclic groups of order $p^n q$, where $p$, $q$ are distinct primes and $n\geq1$.

WebJul 12, 2024 · The Fuglede conjecture states that a set is spectral if and only if it tiles by translation. The conjecture was disproved by Tao for dimensions 5 and higher by giving … WebMay 20, 2024 · In this paper, we show an equi-distributed property in 2-dimensional finite abelian groups Z p n × Z p m, where p is a prime number. By using this equi-distributed property, we prove that Fuglede's spectral set conjecture holds on groups Z p 2 × Z p, namely, a set in Z p 2 × Z p is a spectral set if and only if it is a translational tile.

WebShort description: Mathematical problem. Fuglede's conjecture is a closed problem in mathematics proposed by Bent Fuglede in 1974. It states that every domain of R d (i.e. subset of R d with positive finite Lebesgue measure) is a spectral set if and only if it tiles R d by translation. [1] WebTheorem1.4 Fuglede’s conjecture is true for Zpqrs, where p,q,r,s are different primes. Combining the results in Theorem 1.2 (8) and Theorem 1.4 we obtain the following corollary. Corollary1.5 Fuglede’s conjecture is true for Zpqrs, where p,q,r,s are arbitrary primes.

WebJul 9, 2024 · In the present paper, we will prove that Fuglede’s conjecture in \(\mathbb {Q}_p\) holds. Theorem 1.2. Assume that \(\Omega \subset \mathbb {Q}_{p}\) is a Borel …

WebMay 29, 2024 · Fuglede's spectral set conjecture states that a subset \Omega of a locally compact abelian group G tiles the group by translation if and only if there exists a subset of continuous group characters which is an orthogonal basis of L^2 (\Omega). We prove that Fuglede's conjecture holds on cyclic groups \mathbb {Z}_ {pqr} with p,q,r distinct … horse racing nation 2 6 2023WebFuglede’s conjecture holds for Z 2 p ˆ Zq – Zpq ˆ Zpq, where q and p are different primes. Moreover as we will see in Section 5 that if a set A tiles Z2 p ˆZ2 q, then it tiles with a subgroup as well. 2 Preliminaries and Notation Definition 2.1. Given a finite abelian group G, we can define the character psalms book of the bibleWebAnother is trying to find for which group G, Fuglede's conjecture holds in G. In [7, 8], Fan et al. proved that Fuglede's conjecture holds in Q p , the field of p-adic numbers. We … horse racing nation belmont