三个数字集生成的 Moran 测度无穷正交集的存在性  

The Existence of Infinite Orthogonal Sets of Moran Measures with Three-Element Digit Sets

作　　者：熊婷 

机构地区：[1]福建师范大学数学与统计学院,福建 福州

出　　处：《理论数学》2023年第2期354-363,共10页Pure Mathematics

摘　　要：假设对任意的 n ≥ 1整数 Pn > 1且 Dn ={ 0,an,bn} ⊂ℤ其中 an n n。该文主要研究由整数序列 {pn}n=1∞和数字集序列{Dn}n=1∞生成的 Moran 测度的无穷指数正交集的存在性,得到无穷卷积μ具有无穷指数正交集的充要条件,这为构造此函数空间的谱提供了很好的思路。For n ≥ 1, let Pn > 1 and Dn ={ 0,an,bn} ⊂ℤ, where an n n. In this paper we study the existence of infinite orthogonal exponential sets of moran measures which is generated by the sequence of integers {pn}n=1∞ and the sequence of number sets {Dn}n=1∞. We obtain the necessary and sufficient conditions for infinite convolution μ to have infinite orthogonal exponential sets, this provides a good idea for constructing the spectrum of this function space.

关 键 词：指数正交基 Moran 测度 谱测度 

分 类 号：G63[文化科学—教育学]