Abstract：A Borel probability measure on the n-dimensional Euclidean space is called a spectral measure if the space of square integrable functions admits an family of orthonormal basis. In this paper， the spectral properties of infinite convolutions under the condition of compabitle pairs are studied. By analyzing the spectrality of discrete measures and the exponential orthogonal sets of infinite convolutions and using Lebesgue's dominated convergent theorem， a sufficient condition so that the associated infinite convolutions to be spectral measures is given， which generalizes a criterion due to Strichartz. As applications， a new class of spectral infinite convolutions are constructed.
2025, Vol. 59 
