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Advanced topology on the multiscale sequence spaces S(nu)

Abstract : We put-sue the Study of the multiscale spaces S(v) introduced by Jaffard in the context of multifractal analysis. We give the necessary and Sufficient condition for S(v) to be locally p-convex, and exhibit a sequence of p-norms that defines its natural topology. The strong topological dual of S(v) is identified to another sequence space depending on v, endowed with an inductive limit topology. As a particular case, we describe the dual of a countable intersection of Besov spaces. (C) 2007 Elsevier Inc. All rights reserved.
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Jean-Marie Aubry, Francoise Bastin. Advanced topology on the multiscale sequence spaces S(nu). Journal of Mathematical Analysis and Applications, Elsevier, 2009, 350 (2), pp.439--454. ⟨10.1016/j.jmaa.2007.11.052⟩. ⟨hal-00693133⟩



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