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A CENTURY OF INTERPLAY BETWEEN TAYLOR SERIES, FOURIER SERIES AND BROWNIAN MOTION

Published online by Cambridge University Press:  01 May 1997

JEAN-PIERRE KAHANE
JEAN-PIERRE KAHANE
Affiliation:
Univesité de Paris-Sud, Mathématique Bât. 425, 91405 Orsay Cedex, France
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Abstract

This article is an extended version of a lecture given in Oxford on 12 May 1995 at the invitation of the London Mathematical Society and the British Society for the History of Mathematics.

Contents

1. A few figures

2. Taylor series before 1900. A strange statement of Borel

3. Fourier series before 1900. A strange field

4. Brownian motion around 1900. A rising subject

5. Fourier and Taylor series after 1900. A revival

6. Lacunarity and randomness

7. The appearance of random series of functions

8. The Wiener theory of Brownian motion

9. The merging of Brownian motion and random Fourier series

10. The non-differentiability and local behaviour of Brownian motion

11. Three ways to figure out the Brownian motion

12. The plane Brownian motion

13. Applications of Brownian motion to Taylor series and analytic functions

14. Applications of Brownian motion to Fourier series and harmonic analysis

Type
Review Article
Information
Bulletin of the London Mathematical Society , Volume 29 , Issue 3 , May 1997 , pp. 257 - 279
Copyright
© The London Mathematical Society 1997

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