Diametral dimension of some pseudoconvex multiscale spaces

Jean-Marie Aubry; Françoise Bastin

Studia Mathematica (2010)

  • Volume: 197, Issue: 1, page 27-42
  • ISSN: 0039-3223

Abstract

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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 .

How to cite

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Jean-Marie Aubry, and Françoise Bastin. "Diametral dimension of some pseudoconvex multiscale spaces." Studia Mathematica 197.1 (2010): 27-42. <http://eudml.org/doc/285525>.

@article{Jean2010,
abstract = {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 $S^\{ν\}$.},
author = {Jean-Marie Aubry, Françoise Bastin},
journal = {Studia Mathematica},
keywords = {pseudoconvex space; nuclearity; diametral dimension; multiscale space},
language = {eng},
number = {1},
pages = {27-42},
title = {Diametral dimension of some pseudoconvex multiscale spaces},
url = {http://eudml.org/doc/285525},
volume = {197},
year = {2010},
}

TY - JOUR
AU - Jean-Marie Aubry
AU - Françoise Bastin
TI - Diametral dimension of some pseudoconvex multiscale spaces
JO - Studia Mathematica
PY - 2010
VL - 197
IS - 1
SP - 27
EP - 42
AB - 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 $S^{ν}$.
LA - eng
KW - pseudoconvex space; nuclearity; diametral dimension; multiscale space
UR - http://eudml.org/doc/285525
ER -

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