Scaling of spectra of random convolutions with three-element digit sets

Analysis Mathematica - Tập 47 Số 4 - Trang 781-793 - 2021
S. Chen1, Min-Wei Tang2, C. Wang3
1College of Mathematics and Computational Science, Hunan First Normal University, Changsha, Hunan, P. R. China
2Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP) (Ministry of Education of China), School of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan, P. R. China
3School of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang, P.R. China

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L. X. An, X. Y. Fu and C. K. Lai, On Spectral Cantor-Moran measures and a variant of Bourgain’s sum of sine problem, Adv. Math., 349 (2019), 84–124.

L. X. An and X. G. He, A class of spectral Moran measures, J. Funct. Anal., 266 (2014), 343–354.

L. X. An, X. G. He and K. S. Lau, Spectrality of a class of infinite convolutions, Adv. Math., 283 (2015), 362–376.

X. R. Dai, Spectra of Cantor measures, Math. Ann., 366 (2016), 1621–1647.

X. R. Dai, X. G. He and C. K. Lai, Spectral property of Cantor measures with consecutive digits, Adv. Math., 242 (2013), 187–208.

X. R. Dai, X. G. He and K. S. Lau, On spectral N-Bernoulli measures, Adv. Math., 259 (2014), 511–531.

Q. R. Deng, On the spectra of Sierpinski-type self-affine measures, J. Funct. Anal., 270 (2016), 4426–4442.

D. Dutkay, D. G. Han and Q. Y. Sun, On the spectra of a Cantor measure, Adv. Math., 221 (2009), 251–276.

D. Dutkay and J. Haussermann, Number theory problems from the harmonic analysis of a fractal, J. Number Theory, 159 (2016), 7–26.

D. Dutkay, J. Haussermann and C. K. Lai, Hadamard triples generate self-affine spectral measures, Trans. Amer. Math. Soc., 371 (2019), 1439–1481.

D. Dutkay and I. Kraus, Number theoretic considerations related to the scaling of spectra of Cantor-type measures, Anal. Math., 44 (2018), 335–367.

D. Dutkay and C. K. Lai, Uniformity of measures with Fourier frames, Adv. Math., 252 (2014), 684–707.

D. Dutkay and C. K. Lai, Spectral measures generated by arbitrary and random convolutions, J. Math. Pures. Appl., 107 (2017), 183–204.

Y. S. Fu, X. G. He and Z. X. Wen, Spectra of Bernoulli convolutions and random convolutions, J. Math. Pures Appl., 116 (2018), 105–131.

Y. S. Fu and Z. X. Wen, Spectrality of infinite convolutions with three-element digit sets, Monatsh. Math., 183 (2017), 465–485.

B. Fuglede, Commuting self-adjoint partial differential operators and a group theoretic problem, J. Funct. Anal., 16 (1974), 101–121.

X. G. He, M. W. Tang and Z. Y. Wu, Spectral structure and spectral eigenvalue problems of a class of self-similar spectral measures, J. Funct. Anal., 277 (2019), 3688–3722.

P. Jorgensen, K. Kornelson and K. Shuman, Scaling by 5 on a $${1 \over 4}$$-Cantor measure, Rocky Mountain J. Math., 44 (2014), 1881–1901.

P. Jorgensen and S. Pedersen, Dense analytic subspaces in fractal L2-spaces, J. Anal. Math., 75 (1998), 185–228.

M. N. Kolountzakis and M. Matolcsi, Tiles with no spectra, Forum Math., 18 (2006), 519–528.

I. Łaba and Y. Wang, On spectral Cantor measures, J. Funct. Anal., 193 (2002), 409–420.

J. L. Li, Spectra of a class of self-affine measures, J. Funct. Anal., 260 (2011), 1086–1095.

R. Strichartz, Mock Fourier series and transforms associated with certain Cantor measures, J. Anal. Math., 81 (2000), 209–238.

T. Tao, Fuglede’s conjecture is false in 5 and higher dimensions, Math. Res. Lett., 11 (2004), 251–258.

Z. Y. Wu and M. Zhu, Scaling of spectra of self-similar measures with consecutive digits, J. Math. Anal. Appl., 459 (2018), 307–319.