Advanced topology on the multiscale sequence spaces |
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Authors: | Jean-Marie Aubry Franoise Bastin |
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Institution: | aUniversité de Paris-Est, Laboratoire d'Analyse et de Mathématiques Appliquées, UMR CNRS 8050, 61 av. du Général de Gaulle, F-94010 Créteil, France;bUniversité de Liège, Département de Mathématiques (B37), Grande Traverse, 12, B-4000 Liège, Belgium |
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Abstract: | We pursue the study of the multiscale spaces Sν introduced by Jaffard in the context of multifractal analysis. We give the necessary and sufficient condition for Sν to be locally p-convex, and exhibit a sequence of p-norms that defines its natural topology. The strong topological dual of Sν is identified to another sequence space depending on ν, endowed with an inductive limit topology. As a particular case, we describe the dual of a countable intersection of Besov spaces. |
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Keywords: | Sequence space Local convexity Fré chet space Strong topological dual |
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