The involution kernel and the dual potential for functions in the Walters family

Lucas Y. Hataishi, Artur O. Lopes

Our notation: Points in $\{0,1{\}}^{\mathbb{Z}-\{0\}}=\{0,1{\}}^{\mathbb{N}}\times \{0,1{\}}^{\mathbb{N}}={\Omega }^{-}\times {\Omega }^{+}$, are denoted by $(y|x)=(...,y_2,y_1|x_1,x_2,...)$, where $(x_…