Summation processes viewed from the Fourier properties of continuous unimodular functions on the circle

Volume 95 / 2011

Jean-Pierre Kahane Banach Center Publications 95 (2011), 75-87 MSC: Primary 42A16, 40G99, 26A16. DOI: 10.4064/bc95-0-5


The main purpose of this article is to give a new method and new results on a very old topic: the comparison of the Riemann processes of summation $(R,\kappa)$ with other summation processes. The motivation comes from the study of continuous unimodular functions on the circle, their Fourier series and their winding numbers. My oral presentation in Poznań at the JM–100 conference exposed the ways by which this study was developed since the fundamental work of Brézis and Nirenberg on the topological degree [5]. I shall shorten the historical part in the present article; it can be found in [3], [8] and [9].


  • Jean-Pierre KahaneLaboratoire de Mathématiques
    Université Paris–Sud à Orsay
    Bâtiment 425
    F-91405 Orsay Cedex, France

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