The Spectrality of Infinite Convolutions in ${\mathbb{R}}^d$

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 ${\mathbb{R}}^d$.