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See detailDiametral dimensions of Fréchet spaces
Demeulenaere, Loïc ULg; Frerick, Leonhard; Wengenroth, Jochen

in Studia Mathematica (2016), 234(3), 271-280

This article provides new results concerning the equality between two diametral dimensions. It shows that this equality is true for hilbertizable Fréchet-Schwartz spaces. Moreover, it studies the notion ... [more ▼]

This article provides new results concerning the equality between two diametral dimensions. It shows that this equality is true for hilbertizable Fréchet-Schwartz spaces. Moreover, it studies the notion of prominent sets of Terzioglu and proves that the property "omega bar" of Vogt and Wagner implies the existence of prominent sets. Finally, it shows that the converse implication is true for regular Köthe sequence spaces and brings some spaces with prominent sets but which do not verify “omega bar” (among which there is the space H(D) x H(C)). [less ▲]

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See detailPrevalence of ''nowhere analyticity''
Bastin, Françoise ULg; Esser, Céline ULg; Nicolay, Samuel ULg

in Studia Mathematica (2012), 210(3),

This note brings a complement to the study of genericity of functions which are nowhere analytic mainly in a measure-theoretic sense. We extend this study in Gevrey classes of functions.

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See detailDiametral Dimension of some pseudoconvex multiscale spaces
Aubry, Jean-Marie ULg; Bastin, Françoise ULg

in Studia Mathematica (2010), 197(1), 27-42

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 ... [more ▼]

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 they are always pseudoconvex. We tackle here 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. [less ▲]

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