There are eight-element orthogonal exponentials on the spatial Sierpinski gasket
There are eight-element orthogonal exponentials on the spatial Sierpinski gasket
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空间谢尔宾斯基垫片上存在八元正交指数
DOI：
10.1002/mana.201700471
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发表时间：
2019
影响因子：
1
通讯作者：
Li Jian Lin
中科院分区：
文献类型：
--
作者：
Wang Qi;Li Jian Lin
空间Sierpinski垫片上支持与空间中的扩张矩阵和数字集相对应的自仿射度量，其中是和中单位列向量的标准基。在和的情形下，猜想Hilbert空间中正交指数的基数至多为“4”，其中4是最佳上界。也就是说，所有的四元正交指数集都是极大的。文[1]中给出的一类五元正交指数证明了这一猜想是错误的。在本文中，我们在相应的Hilbert空间中构造了一类八元正交指数来反驳这一猜想。我们还证明了所构造的正交指数集是极大的。
The self‐affine measure corresponding to an expanding matrix and the digit set in the space is supported on the spatial Sierpinski gasket, where are the standard basis of unit column vectors in and . In the case and , it is conjectured that the cardinality of orthogonal exponentials in the Hilbert space is at most “4”, where the number 4 is the best upper bound. That is, all the four‐element sets of orthogonal exponentials are maximal. This conjecture has been proved to be false by giving a class of the five‐element orthogonal exponentials in . In the present paper, we construct a class of the eight‐element orthogonal exponentials in the corresponding Hilbert space to disprove the conjecture. We also illustrate that the constructed sets of orthogonal exponentials are maximal.