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Journal Articles Studia Mathematica Year : 2010

Diametral dimension of some pseudoconvex multiscale spaces

Abstract

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).

Dates and versions

hal-00693035 , version 1 (01-05-2012)

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Jean-Marie Aubry, Francoise Bastin. Diametral dimension of some pseudoconvex multiscale spaces. Studia Mathematica, 2010, 197 (1), pp.27--42. ⟨10.4064/sm197-1-3⟩. ⟨hal-00693035⟩
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