2024 Fuglede's conjecture holds in q p

Fuglede's conjecture holds in q p

Author: wqqr

August undefined, 2024

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 $n\geq1$. 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

WebFuglede’s conjecture holds on Z2 p Z q Gergely Kiss G abor Somlai y January 8, 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 elementary abelian groups the conjecture holds. For Z3 p the problem is still open if p 11. In connection we ... WebIn its full generality, this conjecture is far from being proved and is false for some speciﬁc groups as Tao [19] showed. The question becomes for which group G, Fuglede’s … problem with russia

Fuglede

WebOct 8, 2024 · The 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 … WebThe Nando’s PERi-PERi menu. Order our famous flame-grilled PERi-PERi chicken, signature bowls, sandwiches, sides and more. Dine in or order online. 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. registered herbalist requirements

arXiv:math/0104087v1 [math.CA] 7 Apr 2001

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. WebFinally, we prove Fuglede's conjecture in Q_p without the assumption of compact open sets and also show that the spectral sets (or tiles) are the sets which differ by null sets from compact open sets. registered health information certificationWebJul 12, 2024 · Recently Iosevich, Mayeli and Pakianathan showed that the Fuglede conjecture holds over prime fields when the dimension does not exceed 2. The … registered health information technologist

"WebJun 8, 2003 · We prove Fuglede’s conjecture in Q p which states that 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 translations. ... After collecting the known results we prove that Fuglede’s conjecture holds on Zpq ˆ Zpq – Z 2 p ˆ Z 2 q. 1. View 3 excerpts, cites background; Save. Alert ... " - Fuglede's conjecture holds in q p

Fuglede's conjecture holds in q p

WebPhysical Security Analyst. Booz Allen Hamilton 3.9. Hybrid remote in McLean, VA 22102 +1 location. Greensboro Dr & Solutions Dr. $81,800 - $186,000 a year. The real power … WebJun 19, 2024 · A conjecture of Fuglede suggests that spectra and tiling sets are related. Lagarias and Wang (Invent Math 124(1–3):341–365, 1996) proved that tiling sets are always periodic and are rational. That any spectrum is also a periodic set was proved in Bose and Madan (J Funct Anal 260(1):308–325, 2011) and Iosevich and Kolountzakis (Anal PDE 6: ...

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WebFuglede (1974) conjectured that a domain Omega admits an operator spectrum iff it is possible to tile R^d by a family of translates of Omega. Fuglede proved the conjecture in the special case that the tiling set or the spectrum are lattice subsets of R^d and Iosevich et al. (1999) proved that no smooth symmetric convex body Omega with at least one point … WebAnother 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 …

WebJun 15, 2024 · It was shown that Fuglede's conjecture fails for Z 2 d if d ⩾ 10 [9], and holds if d ⩽ 6 [9], [10]. For 7 ⩽ d ⩽ 9 the answer is not known. Fuglede's conjecture for Z p 3 when p is an odd prime is still wide open, although partial results have been obtained recently for p ⩽ 5 in [3] and for p ⩽ 7 in [6].

WebFuglede's conjecture. Fuglede's conjecture is a closed problem in mathematics proposed by Bent Fuglede in 1974. It states that every domain of (i.e. subset of with positive finite … 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 …

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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 … registered hiv list of namesWebFuglede’s conjecture on cyclic groups of order pnq Romanos Diogenes Malikiosis Mihail N. Kolountzakisy Received 7 December 2016; Published 5 September 2024 Abstract: We show that the spectral set conjecture by Fuglede [6] holds in the setting of cyclic groups of order pnq, where p, q are distinct primes and n 1. This means that a registered hearing aid practitionerWebTheorem1.4 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. problem with router or access pointWebThe question whether Fuglede’s conjecture holds for Z3 p is still widely open, although partial results have been obtained recently for p ≤ 5 in [2] and for p ≤ 7 in [4] . Note that registered health underwriterWeb2DEBASHISH BOSE, C.P. ANIL KUMAR, R. KRISHNAN, AND SHOBHA MADAN Fuglede’s Conjecture. Let be a measurable set in Rd with nite positive measure. Then is spectral if and only if tiles Rd by translations. Fuglede proved this conjecture in Rdunder the additional assumption that the spectrum, or the tiling set, is a d-dimensional lattice … problem with roof valleyWebJul 9, 2024 · Some substantial works have been done for some finite groups [ 2, 13, 16, 24, 25, 35 ]. Let p\ge 2 be prime and \mathbb {Q}_p be the field of p -adic numbers. In the … problem with royal mailWebSep 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 ⋅ ... problem with royal mail tracking