The aim of this expository paper is to introduce the well-behaved uniformizing averages, which are useful in resummation theory. These averages associate three essential, but often antithetic, properties: respecting convolution; preserving realness; reproducing lateral growth. These new objects are serviceable in real resummation and we sketch two typical applications: the unitary iteration of unitary diffeomorphisms and the real normalization of real, local, analytic, vector fields.
@article{urn:eudml:doc:41279,
title = {The well-behaved Catalan and Brownian averages and their applications to real resummation.},
journal = {Publicacions Matem\`atiques},
volume = {41},
year = {1997},
pages = {209-222},
mrnumber = {MR1461652},
zbl = {0883.40007},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41279}
}
Menous, Frédéric. The well-behaved Catalan and Brownian averages and their applications to real resummation.. Publicacions Matemàtiques, Tome 41 (1997) pp. 209-222. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41279/