Winding numbers and Fourier series

Jean-Pierre Kahane (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

This is an expository talk on a topic of classical analysis, arising from the VMO theory of the topological degree due to Brézis and Nirenberg (1995). We sketch the history of the subject and some of its recent developments. The paper is organized as a sequence of questions. Most of them, in particular the last one, deal with Fourier series of continuous functions of constant absolute value. One of them contains new results on the comparison of summation processes.

Mots clés: topological degree; Fourier series; summation processes; BMO; VMO

Domaines: Analyse classique [math.CA]

Jean-Pierre Kahane. Winding numbers and Fourier series. 2009. ⟨hal-00467803⟩