The well-behaved Catalan and Brownian averages and their applications to real resummation
type: Item
instance of: scholarly article
title: The well-behaved Catalan and Brownian averages and their applications to real resummation
zbMATH Open document ID: 0883.40007
DOI: 10.5565/PUBLMAT_41197_13
author: Frédéric Menous
published in: Publicacions Matemàtiques
publication date: 1997-09-04T00:00:00Z
full work available at URL: https://eudml.org/doc/41279
review text: 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.
Mathematics Subject Classification ID: 40C10
zbMATH DE Number: 1057643
zbMATH Keywords: Brownian averages
zbMATH Keywords: Catalan averge
zbMATH Keywords: Ecalle theory
zbMATH Keywords: resummation
zbMATH Keywords: uniformization averages
zbMATH Keywords: Borel transforms
zbMATH Keywords: power series
reviewed by: Jürgen Müller
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1057643