On a theorem of Kaufman: Cantor-type construction of linear fractal Salem sets
type: Item
instance of: scholarly article
title: On a theorem of Kaufman: Cantor-type construction of linear fractal Salem sets
zbMATH Open document ID: 1026.28004
DOI: 10.1007/BF02384771
author: Christian Bluhm
published in: Arkiv för Matematik
publication date: 2003-09-30T00:00:00Z
review text: \textit{R. Kaufman} [Acta Arith. 39, 265-267 (1981; Zbl 0468.10031)] proved that for \(\alpha>0\) the set \(E(\alpha)\) of \(\alpha\)-well approximable numbers in the real axis carries a probability measure with compact support. It shows that the Hausdorff dimension of the support equals its Fourier dimension. In this paper the author tries by modifing Kaufman's construction and casting it in a more geometric form to produce an easier deterministic constructions of linear fractal Salem sets with prescribed dimension.
reviewed by: Jianyong Qiao
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 28A78
Mathematics Subject Classification ID: 43A46
Mathematics Subject Classification ID: 11J83
zbMATH DE Number: 1987636
zbMATH Keywords: Hausdorff dimension
zbMATH Keywords: Fourier dimension
zbMATH Keywords: linear fractal Salem sets
MaRDI profile type: Publication
cites work: Sets of Fractional Dimensions (IV): On Rational Approximation to Real Numbers
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description: scientific article; zbMATH DE number 1987636