ON THE BEURLING DIMENSION OF EXPONENTIAL FRAMES
By Dorin Ervin Dutkay, Deguang Han, Qiyu Sun, E. Weber. 2010
106 citations recorded by the source corpus.
Abstract We study Fourier frames of exponentials on fractal measures associated with a class of affine iterated function systems. We prove that, under a mild technical condition, the Beurling dimension of a Fourier frame coincides with the Hausdorff dimension of the fractal.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/95a38f80d48fd8360dfb0eb35022155297f75e38
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
In Mathematical Physics
Citations in the corpus
- Exponential spectra in L2(μ) (2013, methodology): “proposed to use the Beurling dimension as some general criteria for the existence of Fourier frame [4].”
- Spectra of Cantor measures (2014, methodology): “Spectra of the Cantor measure μb,q have their upper Beurling dimension less than log q/ logb [7], but unlike Fourier frames on the unit interval [23], they could be arbitrarily sparse a nd have zero upper Beurling dimension [3].”
- Weak convergence and spectrality of infinite convolutions (2022, background): “Dutkay, Han, Sun, and Weber [17] related the Beurling dimension of frame spectrum of self-similar measures to the Hausdorff dimension of self-similar sets.”
- On Fourier frame of absolutely continuous measures (2011, methodology): “It is still open whether the one-third Cantor measure will admit any Fourier frame [5,6].”
- Spectral measures with arbitrary Hausdorff dimensions (2014, background): “The above result is established in [10] for maximal orthogon al sets of Cantor measuresμb,d with 2 ≤ b/d ∈ Z.”