Stemming from the study of signals via wavelet coefficients, the spaces are complete metrizable and separable topological vector spaces, parametrized by a function ν, whose elements are sequences indexed by a binary tree. Several papers were devoted to their basic topology; recently it was also shown that depending on ν, may be locally convex, locally p-convex for some p > 0, or not at all, but under a minor condition these spaces are always pseudoconvex. We deal with some more sophisticated properties: their diametral dimensions show that they are Schwartz but not nuclear spaces. Moreover, Ligaud’s example of a Schwartz pseudoconvex non-p-convex space is actually a particular case of .
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm197-1-3,
author = {Jean-Marie Aubry and Fran\c coise Bastin},
title = {Diametral dimension of some pseudoconvex multiscale spaces},
journal = {Studia Mathematica},
volume = {196},
year = {2010},
pages = {27-42},
zbl = {1196.46005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm197-1-3}
}
Jean-Marie Aubry; Françoise Bastin. Diametral dimension of some pseudoconvex multiscale spaces. Studia Mathematica, Tome 196 (2010) pp. 27-42. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm197-1-3/