Menous, Frédéric The well-behaved Catalan and Brownian averages and their applications to real resummation. (English) Zbl 0883.40007 Publ. Mat., Barc. 41, No. 1, 209-222 (1997). 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) Cited in 4 Documents MSC: 40C10 Integral methods for summability Keywords:Brownian averages; Catalan averge; Ecalle theory; resummation; uniformization averages; Borel transforms; power series PDFBibTeX XMLCite \textit{F. Menous}, Publ. Mat., Barc. 41, No. 1, 209--222 (1997; Zbl 0883.40007) Full Text: DOI EuDML