ABSTRACT

At the end of June 1993, a large Conference in Harmonic Analysis was held at the University of Paris-Sud at Orsay to celebrate the prominent role played by Jean-Pierre Kahane and his numerous achievements in this field. Multiplicative processes proved to be of importance, not only in mathematics, but also in modeling Nature. Other multiplicative processes that Jean-Pierre Kahane studied are Mandelbrot martingales. These discrete time martingales, the values of which are measures, were introduced to model intermittency, especially in turbulence, by Benoît Mandelbrot who proved some results and made a number of conjectures. To understand the rich scientific personality of Jean-Pierre Kahane and how it developed as he created the school of harmonic analysis of Orsay, it is necessary to go back to the fifties. It is under the influence of R. Salem that J.-P. Kahane became involved in probability methods in harmonic analysis and, in particular, their use for constructing thin sets.