The well-behaved Catalan and Brownian averages and their applications to real resummation (Q1365664)

The paper enlightens an aspect of J. Ecalle's resummation theory, namely well-behaved uniformization averages. Such averages may be used to determine a (uniform) real function on the positive half axis from the possibly occurring several branches of the Borel transforms of certain formal power series with real coefficients. Well-behaved averages share three essential properties: they respect convolution, they preserve realness and they reproduce lateral growth. Besides the presentation of several examples of uniformization averages (well-behaved or not), the author gives two typical applications: the unitary iteration of unitary diffeomorphisms and the real normalization of real, local, analytic vector fields.