Spectral properties of certain Moran measures with consecutive and collinear digit sets

References

[1] 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. 10.1016/j.aim.2019.04.014Suche in Google Scholar

[2] L.-X. An, L. He and X.-G. He, Spectrality and non-spectrality of the Riesz product measures with three elements in digit sets, J. Funct. Anal. 277 (2019), no. 1, 255–278. 10.1016/j.jfa.2018.10.017Suche in Google Scholar

[3] L.-X. An and X.-G. He, A class of spectral Moran measures, J. Funct. Anal. 266 (2014), no. 1, 343–354. 10.1016/j.jfa.2013.08.031Suche in Google Scholar

[4] L.-X. An, X.-G. He and K.-S. Lau, Spectrality of a class of infinite convolutions, Adv. Math. 283 (2015), 362–376. 10.1016/j.aim.2015.07.021Suche in Google Scholar

[5] L.-X. An, X.-G. He and H.-X. Li, Spectrality of infinite Bernoulli convolutions, J. Funct. Anal. 269 (2015), no. 5, 1571–1590. 10.1016/j.jfa.2015.05.008Suche in Google Scholar

[6] X.-R. Dai, When does a Bernoulli convolution admit a spectrum?, Adv. Math. 231 (2012), no. 3–4, 1681–1693. 10.1016/j.aim.2012.06.026Suche in Google Scholar

[7] X.-R. Dai, Spectra of Cantor measures, Math. Ann. 366 (2016), no. 3–4, 1621–1647. 10.1007/s00208-016-1374-5Suche in Google Scholar

[8] X.-R. Dai, X.-G. He and C.-K. Lai, Spectral property of Cantor measures with consecutive digits, Adv. Math. 242 (2013), 187–208. 10.1016/j.aim.2013.04.016Suche in Google Scholar

[9] X.-R. Dai, X.-G. He and K.-S. Lau, On spectral N-Bernoulli measures, Adv. Math. 259 (2014), 511–531. 10.1016/j.aim.2014.03.026Suche in Google Scholar

[10] X.-R. Dai and Q.-Y. Sun, Spectral measures with arbitrary Hausdorff dimensions, J. Funct. Anal. 268 (2015), no. 8, 2464–2477. 10.1016/j.jfa.2015.01.005Suche in Google Scholar

[11] Q.-R. Deng and K.-S. Lau, Sierpinski-type spectral self-similar measures, J. Funct. Anal. 269 (2015), no. 5, 1310–1326. 10.1016/j.jfa.2015.06.013Suche in Google Scholar

[12] D. Dutkay, J. Haussermann and C.-K. Lai, Hadamard triples generate self-affine spectral measures, Trans. Amer. Math. Soc. 371 (2019), no. 2, 1439–1481. 10.1090/tran/7325Suche in Google Scholar

[13] D. Dutkay and P. Jorgensen, Analysis of orthogonality and of orbits in affine iterated function systems, Math. Z. 256 (2007), no. 4, 801–823. 10.1007/s00209-007-0104-9Suche in Google Scholar

[14] D. Dutkay and C.-K. Lai, Uniformity of measures with Fourier frames, Adv. Math. 252 (2014), 684–707. 10.1016/j.aim.2013.11.012Suche in Google Scholar

[15] K. Falconer, Fractal Geometry, John Wiley, Chichester, 1990. Suche in Google Scholar

[16] X.-Y. Fu, X.-G. He and K.-S. Lau, Spectrality of self-similar tiles, Constr. Approx. 42 (2015), no. 3, 519–541. 10.1007/s00365-015-9306-2Suche in Google Scholar

[17] Y.-S. Fu, X.-G. He and Z.-X. Wen, Spectra of Bernoulli convolutions and random convolutions, J. Math. Pures Appl. (9) 116 (2018), 105–131. 10.1016/j.matpur.2018.06.002Suche in Google Scholar

[18] B. Fuglede, Commuting self-adjoint partial differential operators and a group theoretic problem, J. Funct. Analysis 16 (1974), 101–121. 10.1016/0022-1236(74)90072-XSuche in Google Scholar

[19] L. He and X.-G. He, On the Fourier orthonormal bases of Cantor–Moran measures, J. Funct. Anal. 272 (2017), no. 5, 1980–2004. 10.1016/j.jfa.2016.09.021Suche in Google Scholar

[20] X.-G. He, C.-K. Lai and K.-S. Lau, Exponential spectra in L2⁢(μ), Appl. Comput. Harmon. Anal. 34 (2013), no. 3, 327–338. 10.1016/j.acha.2012.05.003Suche in Google Scholar

[21] T.-Y. Hu and K.-S. Lau, Spectral property of the Bernoulli convolutions, Adv. Math. 219 (2008), no. 2, 554–567. 10.1016/j.aim.2008.05.004Suche in Google Scholar

[22] J. Hutchinson, Fractals and self-similarity, Indiana Univ. Math. J. 30 (1981), no. 5, 713–747. 10.1512/iumj.1981.30.30055Suche in Google Scholar

[23] J. Jacod and P. Protter, Probability Essentials, 2nd ed., Universitext, Springer, Berlin, 2003. 10.1007/978-3-642-55682-1Suche in Google Scholar

[24] P. Jorgensen, S. Pedersen and F. Tian, Spectral theory of multiple intervals, Trans. Amer. Math. Soc. 367 (2015), no. 3, 1671–1735. 10.1090/S0002-9947-2014-06296-XSuche in Google Scholar

[25] P. Jorgensen and S. Pedersen, Dense analytic subspaces in fractal L2-spaces, J. Anal. Math. 75 (1998), 185–228. 10.1007/BF02788699Suche in Google Scholar

[26] M. Kolountzakis and M. Matolcsi, Tiles with no spectra, Forum Math. 18 (2006), no. 3, 519–528. 10.1515/FORUM.2006.026Suche in Google Scholar

[27] I. Łaba and Y. Wang, On spectral Cantor measures, J. Funct. Anal. 193 (2002), no. 2, 409–420. 10.1006/jfan.2001.3941Suche in Google Scholar

[28] C.-K. Lai, K.-S. Lau and H. Rao, Spectral structure of digit sets of self-similar tiles on ℝ1, Trans. Amer. Math. Soc. 365 (2013), no. 7, 3831–3850. 10.1090/S0002-9947-2013-05787-XSuche in Google Scholar

[29] J.-L. Li, On the μM,D-orthogonal exponentials, Nonlinear Anal. 73 (2010), no. 4, 940–951. 10.1016/j.na.2010.04.017Suche in Google Scholar

[30] J.-L. Li, Spectra of a class of self-affine measures, J. Funct. Anal. 260 (2011), no. 4, 1086–1095. 10.1016/j.jfa.2010.12.001Suche in Google Scholar

[31] P. Mattila, Geometry of Sets and Measures in Euclidean Spaces. Fractals and Rectifiability, Cambridge Stud. Adv. Math. 44, Cambridge University, Cambridge, 1995. 10.1017/CBO9780511623813Suche in Google Scholar

[32] R. Strichartz, Mock Fourier series and transforms associated with certain Cantor measures, J. Anal. Math. 81 (2000), 209–238. 10.1007/BF02788990Suche in Google Scholar

[33] R. Strichartz, Convergence of mock Fourier series, J. Anal. Math. 99 (2006), 333–353. 10.1007/BF02789451Suche in Google Scholar

[34] M.-W. Tang and F.-L. Yin, Spectrality of Moran measures with four-element digit sets, J. Math. Anal. Appl. 461 (2018), no. 1, 354–363. 10.1016/j.jmaa.2018.01.018Suche in Google Scholar

[35] T. Tao, Fuglede’s conjecture is false in 5 and higher dimensions, Math. Res. Lett. 11 (2004), no. 2–3, 251–258. 10.4310/MRL.2004.v11.n2.a8Suche in Google Scholar

[36] Z.-Y. Wang, X.-H. Dong and Z.-S. Liu, Spectrality of certain Moran measures with three-element digit sets, J. Math. Anal. Appl. 459 (2018), no. 2, 743–752. 10.1016/j.jmaa.2017.11.006Suche in Google Scholar