In this mainly, but not only, expository paper, revisiting work of M. Herman, A. Rozhdestvenskii and Y. Meyer, we investigate the regularity of functions h solutions to the coboundary equation h(x+ α)-h(x)=f(x), in terms of the function-theoretic properties of the given function f and of the diophantine approximation properties of the irrational number α. We also revisit the equation h(2x)-h(x)=f(x).
Received: September 20, 2019
Published online: April 28, 2019
Hervé Queffélec and Martine QueffélecDépartement de Mathématiques, Université de Lille, Villeneuve d'Ascq, 59855, France.