论文标题
$ \ mathbb {r}^d $中无限卷积的光谱
The Spectrality of Infinite Convolutions in $\mathbb{R}^d$
论文作者
论文摘要
在本文中，我们研究了$ \ mathbb {r}^d $中无限卷积的光谱，其中光谱指的是相应的正方形集成函数空间允许指数函数的家族作为正统基础。假设无限的卷积是由$ \ mathbb {r}^d $中的一对可允许的对生成的。我们通过使用Equi阳性条件和傅立叶变换的积分周期性零集给出了两个足够的条件。通过应用这些结果，我们在$ \ mathbb {r}^d $中显示了某些特定无限卷积的光谱。
In this paper, we study the spectrality of infinite convolutions in $\mathbb{R}^d$, where the spectrality means the corresponding square integrable function space admits a family of exponential functions as an orthonormal basis. Suppose that the infinite convolutions are generated by a sequence of admissible pairs in $\mathbb{R}^d$. We give two sufficient conditions for their spectrality by using the equi-positivity condition and the integral periodic zero set of Fourier transform. By applying these results, we show the spectrality of some specific infinite convolutions in $\mathbb{R}^d$.
