Acknowledgement
The research is supported in part by the Hunan Provincial Department of Education (22B0710) and Hengyang Normal University (2020QD19).
References
- N. Alon and J. H. Spencer, The Probabilistic Method, Wiley-Interscience Series in Discrete Mathematics and Optimization, John Wiley & Sons, Inc., New York, 1992.
- L.-X. An, X. 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. https://doi.org/10.1016/j.aim.2019.04.014
- L.-X. An and X.-G. He, A class of spectral Moran measures, J. Funct. Anal. 266 (2014), no. 1, 343-354. https://doi.org/10.1016/j.jfa.2013.08.031
- J. Bremont, Self-similar measures and the Rajchman property, Ann. H. Lebesgue 4 (2021), 973-1004. https://doi.org/10.5802/ahl.94
- R. Cawley and R. D. Mauldin, Multifractal decompositions of Moran fractals, Adv. Math. 92 (1992), no. 2, 196-236. https://doi.org/10.1016/0001-8708(92)90064-R
- X.-R. Dai, D.-J. Feng, and Y. Wang, Refinable functions with non-integer dilations, J. Funct. Anal. 250 (2007), no. 1, 1-20. https://doi.org/10.1016/j.jfa.2007.02.005
- X.-R. Dai and Q. Sun, Spectral measures with arbitrary Hausdorff dimensions, J. Funct. Anal. 268 (2015), no. 8, 2464-2477. https://doi.org/10.1016/j.jfa.2015.01.005
- H. Davenport, P. Erd˝os, and W. J. LeVeque, On Weyl's criterion for uniform distribution, Michigan Math. J. 10 (1963), 311-314. http://projecteuclid.org/euclid.mmj/1028998917 1028998917
- D. E. Dutkay and C.-K. Lai, Spectral measures generated by arbitrary and random convolutions, J. Math. Pures Appl. (9) 107 (2017), no. 2, 183-204. https://doi.org/10.1016/j.matpur.2016.06.003
- P. Erdos, On a family of symmetric Bernoulli convolutions, Amer. J. Math. 61 (1939), 974-976. https://doi.org/10.2307/2371641
- P. Erdos, On the smoothness properties of a family of Bernoulli convolutions, Amer. J. Math. 62 (1940), 180-186. https://doi.org/10.2307/2371446
- D.-J. Feng, Z. Y. Wen, and J. Wu, Some dimensional results for homogeneous Moran sets, Sci. China Ser. A 40 (1997), no. 5, 475-482. https://doi.org/10.1007/BF02896955
- L. He and X.-G. He, On the Fourier orthonormal bases of Cantor-Moran measures, J. Funct. Anal. 272 (2017), no. 5, 1980-2004. https://doi.org/10.1016/j.jfa.2016.09.021
- S. Hua and W. X. Li, Packing dimension of generalized Moran sets, Progr. Natur. Sci. (English Ed.) 6 (1996), no. 2, 148-152.
- S. Hua, H. Rao, Z. Wen, and J. Wu, On the structures and dimensions of Moran sets, Sci. China Ser. A 43 (2000), no. 8, 836-852. https://doi.org/10.1007/BF02884183
- J. Hutchinson, Fractals and self-similarity, Indiana Univ. Math. J. 30 (1981), no. 5, 713-747. https://doi.org/10.1512/iumj.1981.30.30055
- B. Jessen and A. Wintner, Distribution functions and the Riemann zeta function, Trans. Amer. Math. Soc. 38 (1935), no. 1, 48-88. https://doi.org/10.2307/1989728
- J.-P. Kahane, Sur la distribution de certaines series aleatoires, in Colloque de Theorie des Nombres (Univ. Bordeaux, Bordeaux, 1969), 119-122, Supplement au Bull. Soc. Math. France, Tome 99, Soc. Math. France, Paris, 1971. https://doi.org/10.24033/msmf.42
- J. Li and T. Sahlsten, Fourier transform of self-affine measures, Adv. Math. 374 (2020), 107349, 35 pp. https://doi.org/10.1016/j.aim.2020.107349
- Z. S. Liu, X. H. Dong, and P. F. Zhang, A class of spectral Moran measures on ℝ, Fractals 28 (2020), no. 1, 2050015.
- Z.-Y. Lu, X.-H. Dong, and Z.-S. Liu, Spectrality of Sierpinski-type self-affine measures, J. Funct. Anal. 282 (2022), no. 3, Paper No. 109310, 31 pp. https://doi.org/10.1016/j.jfa.2021.109310
- P. A. P. Moran, Additive functions of intervals and Hausdorff measure, Proc. Cambridge Philos. Soc. 42 (1946), 15-23. https://doi.org/10.1017/s0305004100022684
- R. Salem, Sets of uniqueness and sets of multiplicity, Trans. Amer. Math. Soc. 54 (1943), 218-228. https://doi.org/10.2307/1990330
- B. Solomyak, Fourier decay for self-similar measures, Proc. Amer. Math. Soc. 149 (2021), no. 8, 3277-3291. https://doi.org/10.1090/proc/15515
- P. Varju and H. Yu, Fourier decay of self-similar measures and self-similar sets of uniqueness, Anal. PDE 15 (2022), no. 3, 843-858. https://doi.org/10.2140/apde.2022.15.843