The dimension of a closed subset of \(\mathbb{R}^ n\) and related function spaces
type: Item
instance of: scholarly article
title: The dimension of a closed subset of \(\mathbb{R}^ n\) and related function spaces
zbMATH Open document ID: 0851.46028
DOI: 10.1007/BF01874439
author: Hans Triebel
author: H. Winkelvoß
published in: Acta Mathematica Hungarica
publication date: 1996-11-21T00:00:00Z
review text: Two notions of the dimension of a non-empty closed subset \(F\) of \(\mathbb{R}^n\) with empty interior are introduced. The first is connected with the question of whether, in some Besov function space, there exists a non-trivial singular distribution with support on \(F\). The second is related to \(\varepsilon\)-entropy and \(\varepsilon\)-capacity of \(F\) and its neighbourhood and is connected with atomic representation of function spaces. New Besov function spaces are introduced.
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 54F45
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 55M10
zbMATH DE Number: 794422
zbMATH Keywords: Besov function space
zbMATH Keywords: \(\varepsilon\)-entropy
zbMATH Keywords: \(\varepsilon\)-capacity
reviewed by: John F. Toland
MaRDI profile type: Publication
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cites work: A New Theory of Dimension
cites work: Q5607484
cites work: Q3336200
cites work: Q4003552
cites work: Intrinsic atomic characterizations of function spaces on domains
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description: scientific article; zbMATH DE number 794422