Current Search: Harmonic Analysis -- Tiling -- Fractal (x)
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Title
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Tiling properties of spectra of measures.
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Creator
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Haussermann, John, Dutkay, Dorin, Han, Deguang, Sun, Qiyu, Dogariu, Aristide, University of Central Florida
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Abstract / Description
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We investigate tiling properties of spectra of measures, i.e., sets ? in R with an orthogonal basis in L2 with respect to some finite Borel measure on R. Such measures include Lebesgue measure on bounded Borel subsets, finite atomic measures and some fractal Hausdorff measures. We show that various classes of such spectra of measures have translational tiling properties. This lead to some surprising tiling properties for spectra of fractal measures, the existence of complementing sets and...
Show moreWe investigate tiling properties of spectra of measures, i.e., sets ? in R with an orthogonal basis in L2 with respect to some finite Borel measure on R. Such measures include Lebesgue measure on bounded Borel subsets, finite atomic measures and some fractal Hausdorff measures. We show that various classes of such spectra of measures have translational tiling properties. This lead to some surprising tiling properties for spectra of fractal measures, the existence of complementing sets and spectra for finite sets with the Coven-Meyerowitz property, the existence of complementing Hadamard pairs in the case ofHadamard pairs of size 2,3,4 or 5. In the context of the Fuglede conjecture, we prove that any spectral set is a tile, if the period of the spectrum is 2,3,4 or 5.
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Date Issued
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2014
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Identifier
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CFE0005182, ucf:50656
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Format
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Document (PDF)
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PURL
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http://purl.flvc.org/ucf/fd/CFE0005182
