Size of orthogonal sets of exponentials for the disk
Size of orthogonal sets of exponentials for the disk
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磁盘正交指数集的大小
DOI：
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发表时间：
2011
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通讯作者：
M. N. Kolountzakis
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文献类型：
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作者：
A. Iosevich;M. N. Kolountzakis
假设$ λ subseteq RR^2$具有这样的性质任意两个频率为$ λ $的指数在空间$L^2(D)$中是正交的，其中$D subseteq RR^2$是单位圆盘。已知这样的集合$ λ $是有限的，但不知道它们的大小是否一致有界。我们证明，如果$Lambda$中有两个元素距离$t$，则$Lambda$的大小为$O(t)$。因此，我们改进了Iosevich和Jaming的结果，证明了$Lambda$在任何半径$R$的圆盘上最多有$O(R^{2/3})$个元素。
Suppose $Lambda subseteq RR^2$ has the property that any two exponentials with frequency from $Lambda$ are orthogonal in the space $L^2(D)$, where $D subseteq RR^2$ is the unit disk. Such sets $Lambda$ are known to be finite but it is not known if their size is uniformly bounded. We show that if there are two elements of $Lambda$ which are distance $t$ apart then the size of $Lambda$ is $O(t)$. As a consequence we improve a result of Iosevich and Jaming and show that $Lambda$ has at most $O(R^{2/3})$ elements in any disk of radius $R$.