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PDF(556 KB)
PDF(556 KB)
非谱自仿测度下正交指数函数系的基数
The Cardinality of Orthogonal Exponentials Under the Non-spectral Self-affine Measures
设是μM，D由扩张矩阵M ∈ Mn（Z）和有限数字集D ⊂ Zn通过仿射迭代函数系统{φd（x）=M-1（x+d）}d∈D唯一确定的自仿测度，它的非谱性与相应的平方可积函数构成的Hilbert空间L2（μM，D）中正交指数函数系的有限性或无限性密切相关.通过对数字集D的符号函数mD（x）的零点集合Z（mD）的特征分析以及其中非零中间点（即坐标为0或1/2的点）和非中间点的性质应用，得到了非谱自仿测度下正交指数函数系基数的一个更为精确的估计，改进推广了Dutkay，Jorgensen等人的相关结果.
Let μM,D be the self-affine measure uniquely determined by an expanding matrix M ∈ Mn(Z) and a finite digit set D ⊂ Zn through the affine iterated function system (IFS){φd(x)=M-1(x+d)}d∈D. The non-spectrality of μM,D is directly connected with the finiteness or infiniteness of orthogonal exponentials in the Hilbert space L2(μM,D). We provide a better estimate on the cardinality of μM,D-orthogonal exponentials by characterizing the zero set Z(mD) of the symbol function mD(x) and its middle points. The results here extend the corresponding results of Dutkay, Jorgensen and others.
自仿测度 / 正交指数函数系 / 非谱性 / 数字集 {{custom_keyword}} /
self-affine measures / orthogonal exponentials / non-spectrality / digit set {{custom_keyword}} /
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国家自然科学基金资助项目（11571214）；中央高校基本科研业务费专项基金（GK201601004）
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