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On the Fourier dime...
On the Fourier dimension and a modification
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- Ekström, Fredrik (författare)
- Lund University,Lunds universitet,Matematik LTH,Matematikcentrum,Institutioner vid LTH,Lunds Tekniska Högskola,Mathematics (Faculty of Engineering),Centre for Mathematical Sciences,Departments at LTH,Faculty of Engineering, LTH
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- Persson, Tomas (författare)
- Lund University,Lunds universitet,Dynamiska system,Forskargrupper vid Lunds universitet,Matematik LTH,Matematikcentrum,Institutioner vid LTH,Lunds Tekniska Högskola,Dynamical systems,Lund University Research Groups,Mathematics (Faculty of Engineering),Centre for Mathematical Sciences,Departments at LTH,Faculty of Engineering, LTH
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- Schmeling, Jörg (författare)
- Lund University,Lunds universitet,Dynamiska system,Forskargrupper vid Lunds universitet,Matematik LTH,Matematikcentrum,Institutioner vid LTH,Lunds Tekniska Högskola,Dynamical systems,Lund University Research Groups,Mathematics (Faculty of Engineering),Centre for Mathematical Sciences,Departments at LTH,Faculty of Engineering, LTH
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(creator_code:org_t)
- 2015
- 2015
- Engelska.
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Ingår i: Journal of Fractal Geometry. - 2308-1309. ; 2:3, s. 309-337
- Relaterad länk:
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https://arxiv.org/ab... (free)
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http://dx.doi.org/10...
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https://lup.lub.lu.s...
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https://doi.org/10.4...
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Abstract
Ämnesord
Stäng
- We give a sufficient condition for the Fourier dimension of a countable union of sets to equal the supremum of the Fourier dimensions of the sets in the union, and show by example that the Fourier dimension is not countably stable in general. A natural approach to finite stability of the Fourier dimension for sets would be to try to prove that the Fourier dimension for measures is finitely stable, but we give an example showing that it is not in general. We also describe some situations where the Fourier dimension for measures is stable or is stable for all but one value of some parameter. Finally we propose a way of modifying the definition of the Fourier dimension so that it becomes countably stable, and show that for each s there is a class of sets such that a measure has modied Fourier dimension greater than or equal to s if and only if it annihilates all sets in the class.
Ämnesord
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Nyckelord
- Stability of Fourier dimension
- modified Fourier dimension
Publikations- och innehållstyp
- art (ämneskategori)
- ref (ämneskategori)
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