Steéphanie Nivoche (Université Côte
d'Azur)
Title: New solution of a problem of Kolmogorov on width asymptotics in
holomorphic function spaces.
Abstract:
In this talk we will discuss the notion of epsilon-entropy and the
related notion of n-widths introduced by Kolmogorov in the 1950s,
as a measure of the complexity of compact sets in a metric space. We
will then discuss a new proof for a problem originally raised by Kolmogorov
on the precise asymptotics of the epsilon-entropy of compact sets in
spaces of holomorphic functions which relies on a reformulation in terms
of Toeplitz operators on weighted Bergman spaces, exhaustion procedures
by special holomorphic polyhedra and ideas from pluripotential theory.