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arXiv · 1008.4304

Bessel sequences of exponentials on fractal measures

Dorin Ervin Dutkay·Deguang Han·Eric Weber
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Abstract

Jorgensen and Pedersen have proven that a certain fractal measure $ν$ has no infinite set of complex exponentials which form an orthonormal set in $L^2(ν)$. We prove that any fractal measure $μ$ obtained from an affine iterated function system possesses a sequence of complex exponentials which forms a Riesz basic sequence, or more generally a Bessel sequence, in $L^2(μ)$ such that the frequencies have positive Beurling dimension.

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Dorin Ervin Dutkay, Deguang Han, Eric Weber. 2010-08-25. Bessel sequences of exponentials on fractal measures. https://arxiv.org/abs/1008.4304

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