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Diametral dimension of some pseudoconvex multiscale spaces

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Aubry J.-M., Bastin F.

Studia Mathematica

2010

tom 197

nr 1

27-42

Stemming from the study of signals via wavelet coefficients, the spaces $S^{ν}$ are complete metrizable and separable topological vector spaces, parametrized by a function ν, 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 ν, $S^{ν}$ 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 $S^{ν}$.

Prevalence of "nowhere analyticity"

81%

Bastin F., Esser C., Nicolay S.

Studia Mathematica

2012

tom 210

nr 3

239-246

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 to Gevrey classes of functions.

Ograniczanie wyników

2 Studia Mathematica

2 Bastin F.

1 Aubry J.-M.

1 Esser C.

1 Nicolay S.

1 2012

1 2010

Wyniki wyszukiwania

Diametral dimension of some pseudoconvex multiscale spaces

Prevalence of "nowhere analyticity"