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

• Autorzy: Jean-Pierre Kahane
• Języki publikacji: EN

Abstrakty

EN

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,κ) 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].

Kategorie tematyczne

• 40G99: None of the above, but in this section
• 26A16: Lipschitz (H\"older) classes
• 42A16: Fourier coefficients, Fourier series of functions with special properties, special Fourier series

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2011
• Tom: 95
• Numer: 1
• Strony: 75-87

Daty

wydano

2011

Twórcy

autor

Jean-Pierre Kahane

• Laboratoire de Mathématiques, Université Paris-Sud à Orsay, Bâtiment 425, F-91405 Orsay Cedex, France

Identyfikatory

DOI

10.4064/bc95-0-5