Study of almost everywhere convergence of series by mean of martingale methods

Christophe Cuny (1) , Ai Hua Fan (2)

1 MICS - Mathématiques et Informatique pour la Complexité et les Systèmes
2 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352

Martingale methods are used to study the almost everywhere convergence of general function series. Applications are given to ergodic series, which improves recent results of Fan (2015), and to dilated series, including Davenport series, which completes results of Gaposhkin (1967) (see also Gaposhkin (1968)). Applications are also given to the almost everywhere convergence with respect to Riesz products of lacunary series. (C) 2016 Elsevier B.V. All rights reserved.

Keywords: Ergodic series; Dilated series; Martingale; Transfer operator

Domains: Mathematics [math]

Christophe Cuny, Ai Hua Fan. Study of almost everywhere convergence of series by mean of martingale methods. Stochastic Processes and their Applications, 2017, 127 (8), pp.2725-2750. ⟨10.1016/j.spa.2016.12.006⟩. ⟨hal-02404277⟩