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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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Peer Reviewed
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.

Detailed reference viewed: 45 (21 ULg)
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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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