An extension of Laba-Wang's theorem
An extension of Laba-Wang's theorem
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拉巴-旺定理的推广
DOI：
10.1016/j.jmaa.2020.124380
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发表时间：
2020-11-15
影响因子：
1.3
通讯作者：
Tang, Min-Wei
中科院分区：
文献类型：
--
作者：
Fu, Yan-Song;Tang, Min-Wei
对于正整数B >= 2，Z的两个有限子集D，C具有相同的基数，如果矩阵[e（2 pi idc/B）]（d是D的一个元素，c是C的一个元素）是正交的，则称对（B（-1）D，C）是相容对。设N的{n（j）}（j=1）（无穷）子集为任意正整数序列.本文证明了在相容对（B（-1）D，C）的条件下，齐次Moran测度μ（B，D，{nj}）= delta（B）（- n1 D）* delta（B -（n1 + n2）D）*. * delta（B -（n1 + n2 +.）nk）D）*.具有由指数组成的标准正交基。这推广了Laba和Wang（2002）[22]的一个结果，并建立了Fu和Wen（2015）[18]猜想1.1的证明。(C)2020爱思唯尔公司All rights reserved.
For a positive integer b >= 2 and two finite subsets D, C of Z with the same cardinality, we say that the pair (b(-1) D, C) is a compatible pair if the matrix [e(2 pi idc/b)](d is an element of D, c is an element of C )is orthogonal. Let {n(j)}(j=1)(infinity) subset of N be any sequence of positive integers. In this paper we will show, under the condition of compatible pair (b(-1) D, C), that the homogeneous Moran measuremu(b, D, {nj}) = delta(b) (- n1 D) * delta(b - (n1 + n2) D) * ...* delta(b - (n1 + n2 + ... nk) D )* ...has an orthonormal basis consisting of exponentials. This extends a result of Laba and Wang (2002) [22] and establishes the proof of Conjecture 1.1 of Fu and Wen (2015) [18]. (C) 2020 Elsevier Inc. All rights reserved.