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



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