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SPECTRALITY AND NON-SPECTRALITY OF PLANAR SELF-SIMILAR MEASURES WITH FOUR-ELEMENT DIGIT SETS
Fractals ( IF 3.3 ) Pub Date : 2020-07-13 , DOI: 10.1142/s0218348x20501303
SI CHEN 1 , MIN-WEI TANG 2
Affiliation  

Let [Formula: see text] be the unit matrix and [Formula: see text]. In this paper, we consider the self-similar measure [Formula: see text] on [Formula: see text] generated by the iterated function system [Formula: see text] where [Formula: see text]. We prove that there exists [Formula: see text] such that [Formula: see text] is an orthonormal basis for [Formula: see text] if and only if [Formula: see text] for some integer [Formula: see text].

中文翻译:

四元数集平面自相似量度的光谱与非光谱

设[公式:见正文]为单位矩阵,[公式:见正文]。在本文中,我们考虑由迭代函数系统[公式:见文本]生成的[公式:见文本]上的自相似度量[公式:见文本],其中[公式:见文本]。我们证明存在 [Formula: see text] 使得 [Formula: see text] 是 [Formula: see text] 的标准正交基当且仅当 [Formula: see text] 对于某个整数 [Formula: see text]。
更新日期:2020-07-13
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