The heritage of Fourier. (English) Zbl 1109.01008

Kahane, Jean-Pierre

Benedicks, Michael (ed.) et al., Perspectives in analysis. Essays in honor of Lennart Carleson’s 75th birthday. Proceedings of the conference, Stockholm, Sweden, May 26–28, 2003. Berlin: Springer (ISBN 3-540-30432-0/hbk). Math. Phys. Stud. 27, 83-95 (2005).

The author concentrates on a narrow but important part of the scientific heritage of Fourier, namely the expansion of a function into a trigonometric series and the formulas for computing the coefficients. About the way of thinking of Fourier his general theme is that it has been disregarded for a long time, and that it became very popular quite recently. The main part of the article is made of quotations and comments (Victor Hugo, Jacobi, Fourier, Dirichlet and Riemann). Sect. 3 is devoted to the Riemann theory of trigonometric series and Sect. 4 to the convergence problem after Dirichlet (the Carleson theorem, variations about convergence). The end, Sect. 5, is about the coming back of Fourier.
For the entire collection see [Zbl 1089.00008].

Reviewer: Ülo Lumiste (Tartu)

MSC:

01A55	History of mathematics in the 19th century
42-03	History of harmonic analysis on Euclidean spaces
01A60	History of mathematics in the 20th century
42A20	Convergence and absolute convergence of Fourier and trigonometric series

Keywords:

heritage of Fourier; trigonometric series