Fuglede's conjecture holds in q p
WebFuglede'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 Lebesgue measure) … 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 also know that ...
Fuglede's conjecture holds in q p
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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 … 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 …
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 … Web2DEBASHISH 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 …
WebFuglede’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
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 ...
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. patio container vegetable gardeningWebMay 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. patio conservatoryWebFuglede’s conjecture holds in Qp, the field of p-adic numbers. We also know that Fuglede’s conjecture holds in the following finite Abelian groups: Zd p (p = 2 and d ≤ 6; p is an odd prime ガスショップ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]. ガスショップ女池WebAbstract: Fuglede’s spectral set conjecture states that a subset W of a locally compact abelian group G tiles the group by translation if and only if there exists a subset of … かずさん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] かずさん亭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 ⋅ ... patio contractors peoria il