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| HAL: hal-00693035, version 1 |
| DOI: 10.4064/sm197-1-3 |
| Detailed view |  Export this paper |
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| Studia Mathematica 197, 1 (2010) 27--42 |
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| Diametral dimension of some pseudoconvex multiscale spaces |
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| Jean-Marie Aubry 1Francoise Bastin |
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| (2010) |
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| 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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| 1: | Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA) |
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Université Paris-Est Marne-la-Vallée (UPEMLV) – Université Paris-Est Créteil Val-de-Marne (UPEC) – CNRS : UMR8050 – Fédération de Recherche Bézout |
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| Subject | : | Mathematics/Mathematical Physics |
| hal-00693035, version 1 | |
| http://hal-upec-upem.archives-ouvertes.fr/hal-00693035 | |
| oai:hal-upec-upem.archives-ouvertes.fr:hal-00693035 | |
| From: Admin Lama | |
| Submitted for: | |
| Submitted on: Tuesday, 1 May 2012 19:39:59 | |
| Updated on: Tuesday, 1 May 2012 19:39:59 | |
