Eigenvalues of transformations arising from irrational rotations and step functions. (Valeurs propres de transformations liées aux rotations irrationnelles et aux fonctions en escalier)

Melanie Guenais, Francois Parreau

Given an irrational rotation $T$ on $\M T$ we settle necessary and sufficient conditions on a step function $\varphi$ and $t\in \M T$ for the existence of measurable solutions to the coh…