由二元和三元数字集生成的莫兰型测度的谱性
Spectrality of Moran-Type Measures Generated by Two-Element and Three-Element Digit Sets
浏览论文内容
中文总结 AI 辅助
研究由二元和三元数字集生成的莫兰型测度的谱性，核心方法是依据卷积中各项傅里叶变换零集的因子数量判定，贡献为给出其为谱测度的充要条件，并揭示无哈达玛三元组时问题更复杂困难。
中文摘要 AI 辅助
给出了由二元和三元数字集生成的莫兰型测度为谱测度的充要条件。主要结果表明，这种莫兰型测度的谱性完全由卷积中各项傅里叶变换零集中的2-因子和3-因子的数量决定。证明表明，在不存在哈达玛三元组的情况下，该问题比存在哈达玛三元组的情况要复杂和困难得多。
英文摘要
The necessary and sufficient conditions for the Moran-type measures generated by two-element and three-element digit sets to be spectral have been given. The main result indicates that the spectrality of such a Moran-type measure is completely determined by the number of 2-factors and 3-factors in the zero set of the Fourier transform of each term in the convolution. The proof shows that, without the existence of Hadamard triples, the problem becomes much more complicated and difficult than the case with the existence of Hadamard triples.
