In this article, we extend the theory of multiplicative chaos for positive definite functions in R of the form f(x) = λ ln T |x| + g(x) where g is a continuous and bounded function. The construction is simpler and more general than the one defined by Kahane in 1985. As main application, we give a rigorous mathematical meaning to the Kolmogorov-Obukhov model of energy dissipation in a turbulent ...

I am one of a growing number of research mathematicians who are substantially engaged with school mathematics education. Such outreach has a long and honorable tradition. In this lecture, I illustrate some of the ways that I think this can be helpful, and even essential. Upon his retirement in 1990 as president of the ICMI, Jean Pierre Kahane spoke perceptively of the intimate connection betwee...

This is Part II of the two-part feature on Paul Erdős following his centennial. Part I had contributions from Krishnaswami Alladi and Steven G. Krantz, Vera T. Sós and László Lovász, Ronald Graham and Joel Spencer, Jean-Pierre Kahane, and Mel Nathanson. Here in Part II we have six articles from contributors Noga Alon, Dan Goldston, András Sárközy, József Szabados, Gérald Tenenbaum, and Stephan ...

We consider a generalized version of the sign uncertainty principle for Fourier transform, first proposed by Bourgain, Clozel and Kahane in 2010 revisited Cohn Goncalves 2019. In our setup, signs function its transform resonate with generic given $P$ outside ball. One essentially wants to know if how soon this resonance can happen, when facing suitable competing weighted integral condition. The...

In this article, we extend the theory of multiplicative chaos for positive definite functions in R of the form f(x) = λ ln T |x| + g(x) where g is a continuous and bounded function. The construction is simpler and more general than the one defined by Kahane in 1985. As main application, we give a rigorous mathematical meaning to the Kolmogorov-Obukhov model of energy dissipation in a turbulent ...

Aleksandrov, Anderson and Nicolau have found examples of inner functions that are in the little Bloch space with a specific rate of convergence to zero. As a corollary they obtain positive singular measures defined in the boundary of the unit disc that are simoultaneously symmetric and Kahane. Nevertheless their construction is very indirect. We give an explicit example of such measures by mean...