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The well-behaved Catalan and Brownian averages and their applications to real resummation. (English) Zbl 0883.40007

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.
Reviewer: J.Müller (Trier)

MSC:

40C10 Integral methods for summability
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