Diophantine approximation and coboundary equations

Hervé Queffélec and Martine Queffélec – GJM, Volume 4, Issue 1 (2019), 1-17.

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 Queffélec
Département de Mathématiques, Université de Lille, Villeneuve d'Ascq, 59855, France.


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