论文标题
无限卷积和随机卷积的光谱
Spectrality of Infinite Convolutions and Random Convolutions
论文作者
论文摘要
在本文中，我们探讨了光谱措施，其正方形的空间承认指数函数的家族是正常的基础。最后，我们表明，鉴于有限的许多可接受对，几乎所有随机的卷积都是光谱措施。此外，在某些特殊情况下，我们给出了随机卷积的光谱的完整表征。
In this paper, we explore spectral measures whose square integrable spaces admit a family of exponential functions as an orthonormal basis.Our approach involves utilizing the integral periodic zeros set of Fourier transform to characterize spectrality of infinite convolutions generated by a sequence of admissible pairs.Then we delve into the analysis of the integral periodic zeros set. Finally, we show that given finitely many admissible pairs, almost all random convolutions are spectral measures. Moreover, we give a complete characterization of spectrality of random convolutions in some special cases.
