Wavelet Bases Solving Infrared Divergence Phenomenon
Béatrice Vedel, Université de Picardie-Jules Verne, Amiens, France

Seminar • 19 July 2007 • BM 5.202

Abstract
The infrared divergence phenomenon often appears in the wavelet analysis of self-similar objects (solutions of PDE, homogeneous functional spaces, self-similar stochastic processes, ...). These objects -built as "fractional primitive" of classical objects (Lebesgue spaces, white noise ) are a priori not defined in the sense of the tempered distributions and their wavelet expansions might diverge - because of the low-frequency (infrared) part. Focusing on the cases of the homogeneous Sobolev spaces and the Mumford process, we will see how to define them in the sense of distributions - when it is possible (works of G. Boudaud) and we will give an adapted wavelet analysis of them.