Bessel sequences of exponentials on fractal measures
Journal of Functional Analysis(2011)
摘要
Jorgensen and Pedersen have proven that a certain fractal measure ν has no infinite set of complex exponentials which form an orthonormal set in L2(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 L2(μ) such that the frequencies have positive Beurling dimension.
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关键词
Fractal,Iterated function system,Frame,Bessel sequence,Riesz basic sequence,Beurling dimension
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