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- Publisher
- Wiley
- Copyright
- © London Mathematical Society
- ISSN
- 0024-6093
- eISSN
- 1469-2120
- DOI
- 10.1112/blms/8.2.145
- Publisher site
- See Article on Publisher Site
Abstract
JEAN-PIERRE KAHANE This is an account of an informal talk given at one of the Durham Conferences of the London Mathematical Society, July 1974. I have made no attempt to transform it into an organized paper, with the hope and the excuse that the easier the writing is, the easier the reading will be. The subject is very rich. I selected only three topics in classical analysis which are closely related to Brownian motion: (1) nowhere differentiable functions, (2) totally disconnected perfect sets, (3) analytic functions of one complex variable. On each of these topics, the Brownian motion sheds much light, and there are interesting new results. 1. Nowhere differentiable functions Weierstrass gave his celebrated example of a continuous nowhere differentiable function in 1872. It was regarded as a curiosity at the time, a kind of a mathematical monster. A geometrical construction of a nowhere differentiable simple curve was described by Von Koch in 1904. Maybe it is worthwhile to look at Von Koch's curve, if only because it apparently attracted the attention of Paul L6vy as a child. I hope the adjacent drawing explains how to obtain Von Koch's curve. It has infinite length, vanishing area, and a
Journal
Bulletin of the London Mathematical Society – Wiley
Published: Jul 1, 1976