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

摘要: 假设对任意的 n ≥ 1整数 P_n > 1且 D_n ={ 0,a_n,b_n} ⊂ℤ其中 a_n < b_n < p_n。该文主要研究由整数序列 {p_n}_n=1^∞和数字集序列{D_n}_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。

Abstract: For n ≥ 1, let P_n > 1 and D_n ={ 0,a_n,b_n} ⊂ℤ, where a_n < b_n < p_n. In this paper we study the existence of infinite orthogonal exponential sets of moran measures which is generated by the sequence of integers {p_n}_n=1^∞ and the sequence of number sets {D_n}_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.