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

In this paper, we study the spectrality of infinite convolutions in \({\mathbb {R}}^d\) ${\mathbb{R}}^d$ , 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 \({\mathbb {R}}^d\) ${\mathbb{R}}^d$ . 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 \({\mathbb {R}}^d\) ${\mathbb{R}}^d$ .