Reference : Diametral Dimension of some pseudoconvex multiscale spaces
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/2268/29728
Diametral Dimension of some pseudoconvex multiscale spaces
English
Aubry, Jean-Marie mailto [Paris 12 Créteil > LAMA > Analyse > >]
Bastin, Françoise mailto [Université de Liège - ULg > Département de mathématique > Analyse, analyse fonctionnelle, ondelettes >]
2010
Studia Mathematica
197
1
27-42
Yes (verified by ORBi)
International
0039-3223
1730-6337
Poland
[en] Stemming from the study of signals via wavelet coefficients, the spaces S\nu are complete metrizable and separable topological vector spaces, parametrized by a function \nu, 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 \nu, S\nu may be locally convex, locally p-convex for some p > 0, or not at all, but under a minor condition they are always pseudoconvex. We tackle here 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 S\nu.
http://hdl.handle.net/2268/29728

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