6 papers
Conditions for Beurling's integers to have a density
Jean-Pierre Kahane
In 1997 H.G.Diamond gave a condition on Beurling's generalized prime numbers in order that the corresponding generalized integers have a density. We give a new proof of this condit…
On Euler's example of a completely multiplicative function with sum 0
Jean-Pierre Kahane, Eric Saïas
Euler wrote a formula expressing that l(n)/n is a completely multiplicative function with sum 0 (a CMO function) , where l(n) is the completely multiplicative function equal to -1…
Turan's method and compressive sampling
Jean-Pierre Kahane
Turan's method, as expressed in his books, is a careful study of trigonometric polynomials from different points of view. The present article starts from a problem asked by Turan:…
Winding numbers and Fourier series
Jean-Pierre Kahane
This is an expository talk on a topic of classical analysis, arising from the VMO theory of the topological degree due to Brézis and Nirenberg (1995). We sketch the history of the…
Restrictions of continuous functions
Jean-Pierre Kahane, Yitzhak Katznelson
Given a continuous real-valued function on [0, 1], and a closed subset E \subset [0, 1] we denote by f E the restriction of f to E, that is, the function defined only on E that tak…
A Brownian quasi-helix in IR4, built from an automatic sequence
Jean-Pierre Kahane
We describe a brownian quasi-helix in R^4 by means of an automatic sequence