In this volume, the authors prove that the solutions of a cohomological equation of complex dimension one and in the analytic category have a monogenic dependence on the parameter, and we investigate the question of their quasianalyticity.Introduction; Monogenic properties of the solutions of the cohomological equation; Carleman classes at diophantine points; Resummation at resonances and constant-type points; Conclusions and applications; Appendix; Bibliography