An extension of the Wiener-Wintner ergodic theorem for pointwise jointly ergodic systems and its applications

Michihiro Hirayama, Younghwan Son

A joint measure-preserving system is $(X,\mathcal{B},\hat{I}{¼}_1,\dots ,\hat{I}{¼}_k,T_1,\dots ,T_k)$, where each $(X,\mathcal{B},\hat{I}{¼}_i,T_i)$ is a measure-preserving system and…