Diametral dimension of some pseudoconvex multiscale spaces

Tom 197 / 2010

Jean-Marie Aubry, Françoise Bastin Studia Mathematica 197 (2010), 27-42 MSC: 46A16, 46A45, 46A11, 46A13. DOI: 10.4064/sm197-1-3


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 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 $S^{\nu }$.


  • Jean-Marie AubryLab. Anal. Math. Appl. (UMR CNRS 8050)
    Université Paris-Est
    61 av. du Général de Gaulle
    F-94010 Créteil, France
  • Françoise BastinDépartement de Mathématique (B37)
    Université de Liège
    Grande Traverse, 12
    B-4000 Liège, Belgique

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