Spectral property of the Bernoulli convolutions

By Tianyou Hu, Ka-Sing Lau. 2008

190 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4c0f3f43b76e08256824c9ce49d4a0ff8eba1a84

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

1. Xin-Rong Dai
2. Xinggang He
3. Chun-Kit Lai
4. Xiaoye Fu
5. Qiyu Sun
6. Ka-Sing Lau
7. Li-Xiang An
8. Dorin Ervin Dutkay

In Geometry and Topology

1. Xin-Rong Dai
2. Chun-Kit Lai
3. Xinggang He
4. Ka-Sing Lau

In Mathematical Physics

1. Xin-Rong Dai
2. Xinggang He
3. Chun-Kit Lai
4. Xiaoye Fu
5. Qiyu Sun
6. Ka-Sing Lau
7. Li-Xiang An
8. De-Jun Feng

Citations in the corpus

• On Fourier frame of absolutely continuous measures (2011, background): “λ) of the Bernoulli convolutions for which there are infinitely many such orthogonal sets [11].”
• Exponential spectra in L2(μ) (2013, background): “This raises the very interesting question on the existence of an exponential Riesz basis or a Fourier frame for such measures, and more generally for the self-similar measures [15,16,6,25, 10].”
• Spectral measures with arbitrary Hausdorff dimensions (2014, background): “Since then, various singular spectral measures on self-similar/self-affine fractal sets have been found, see for instance [3–6,9,11,15–17,19,21,22,24,26,27,30,34].”
• Spectrality of Self-Similar Tiles (2013, background): “The problem also led to the study of spectral property of discrete integer tiles [12,33,40] and the Cantor-type singularly continuous measures [1,4–6,8,9,18,23,29,41].”
• When does a Bernoulli convolution admit a spectrum (2012, background): “1, we first recall two results on Bernoulli convolutions in [11,15].”
• Spectra of a class of self-affine measures (2011, unknown): “The other results concerning the spectral property of the Bernoulli convolutions have been obtained in [12,9,7,6,13].”
• Spectral property of Cantor measures with consecutive digits (2012, background): “ and other generalized types of Fourier expansions like the Fourier frames and Riesz bases ([DHJ], [DHSW], [DL], [HLL], [IP], [JKS] [L a], [L aW], [Lai], [Li1], [Li2], and the references therein). In [HuL], Hu and Lau made a start in studying the spectral properties of Bernoulli convolutions, the si”