Abstract
Let the self-affine measure
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11971500
Award Identifier / Grant number: 11831007
Award Identifier / Grant number: 11401053
Award Identifier / Grant number: 17B158
Award Identifier / Grant number: 14C0046
Funding statement: The first author is supported by the NNSF of China (no. 11971500). The second author is supported by the NNSF of China (no. 11831007), by the Hunan Provincial NSF (no. 2019JJ20012) and by the SRF of Hunan Provincial Education Department (no. 17B158). The corresponding author is supported by the NNSF of China (no. 11401053) and by the SRF of Hunan Provincial Education Department (no. 14C0046).
References
[1] 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.2015.07.021Search in Google Scholar
[2] X.-R. Dai, When does a Bernoulli convolution admit a spectrum?, Adv. Math. 231 (2012), no. 3–4, 1681–1693. 10.1016/j.aim.2012.06.026Search in Google Scholar
[3] 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.2013.04.016Search in Google Scholar
[4] 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.2014.03.026Search in Google Scholar
[5] Q.-R. Deng, Spectrality of one dimensional self-similar measures with consecutive digits, J. Math. Anal. Appl. 409 (2014), no. 1, 331–346. 10.1016/j.jmaa.2013.07.046Search in Google Scholar
[6] Q.-R. Deng, On the spectra of Sierpinski-type self-affine measures, J. Funct. Anal. 270 (2016), no. 12, 4426–4442. 10.1016/j.jfa.2016.03.006Search in Google Scholar
[7] 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.2015.06.013Search in Google Scholar
[8] D. E. 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/7325Search in Google Scholar
[9] D. E. Dutkay and P. E. T. Jorgensen, Analysis of orthogonality and of orbits in affine iterated function systems, Math. Z. 256 (2007), no. 4, 801–823. 10.1007/s00209-007-0104-9Search in Google Scholar
[10] D. E. Dutkay and P. E. T. Jorgensen, Fourier frequencies in affine iterated function systems, J. Funct. Anal. 247 (2007), no. 1, 110–137. 10.1016/j.jfa.2007.03.002Search in Google Scholar
[11] B. Fuglede, Commuting self-adjoint partial differential operators and a group theoretic problem, J. Funct. Anal. 16 (1974), 101–121. 10.1016/0022-1236(74)90072-XSearch in Google Scholar
[12] 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.2008.05.004Search in Google Scholar
[13] J. E. Hutchinson, Fractals and self-similarity, Indiana Univ. Math. J. 30 (1981), no. 5, 713–747. 10.1512/iumj.1981.30.30055Search in Google Scholar
[14]
P. E. T. Jorgensen and S. Pedersen,
Dense analytic subspaces in fractal
[15] M. N. Kolountzakis and M. Matolcsi, Complex Hadamard matrices and the spectral set conjecture, Collect. Math. (2006), no. Vol. Extra, 281–291. Search in Google Scholar
[16] M. N. Kolountzakis and M. Matolcsi, Tiles with no spectra, Forum Math. 18 (2006), no. 3, 519–528. 10.1515/FORUM.2006.026Search in Google Scholar
[17] I. Ł aba and Y. Wang, On spectral Cantor measures, J. Funct. Anal. 193 (2002), no. 2, 409–420. 10.1006/jfan.2001.3941Search in Google Scholar
[18] J.-L. Li, Non-spectral problem for a class of planar self-affine measures, J. Funct. Anal. 255 (2008), no. 11, 3125–3148. 10.1016/j.jfa.2008.04.001Search in Google Scholar
[19] J.-L. Li, Spectra of a class of self-affine measures, J. Funct. Anal. 260 (2011), no. 4, 1086–1095. 10.1016/j.jfa.2010.12.001Search in Google Scholar
[20] J.-L. Li, Non-spectrality of self-affine measures on the spatial Sierpinski gasket, J. Math. Anal. Appl. 432 (2015), no. 2, 1005–1017. 10.1016/j.jmaa.2015.07.032Search in Google Scholar
[21] J.-C. Liu, X.-H. Dong and J.-L. Li, Non-spectral problem for the planar self-affine measures, J. Funct. Anal. 273 (2017), no. 2, 705–720. 10.1016/j.jfa.2017.04.003Search in Google Scholar
[22] Z.-Y. Lu, X.-H. Dong and P.-F. Zhang, Non-spectrality of self-affine measures on the three-dimensional Sierpinski gasket, Forum Math. 31 (2019), no. 6, 1447–1455. 10.1515/forum-2019-0062Search in Google Scholar
[23] M. B. Nathanson, Elementary Methods in Number Theory, Grad. Texts in Math. 195, Springer, New York, 2000. Search in Google Scholar
[24] F. P. Ramsey, On a Problem of Formal Logic, Proc. London Math. Soc. (2) 30 (1929), no. 4, 264–286. 10.1007/978-0-8176-4842-8_1Search in Google Scholar
[25] 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.a8Search in Google Scholar
[26]
Z.-Y. Wang, Z.-M. Wang, X.-H. Dong and P.-F. Zhang,
Orthogonal exponential functions of self-similar measures with consecutive digits in
[27]
Z. H. Yan,
Spectrality of certain fractal measures on
© 2021 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Approximating pointwise products of quasimodes
- On the group of a rational maximal bifix code
- Hörmander type multiplier theorems on bi-parameter anisotropic Hardy spaces
- Newton’s method for nonlinear stochastic wave equations
- On the classification of Schreier extensions of monoids with non-abelian kernel
- Smoothness filtration of the magnitude complex
- Varieties of nilpotent Lie superalgebras of dimension ≤ 5
- The Dual Baer Criterion for non-perfect rings
- Spectral property of the planar self-affine measures with three-element digit sets
- Spectral properties of certain Moran measures with consecutive and collinear digit sets
- Envelopes of circles and spacelike curves in the Lorentz–Minkowski 3-space
- A polynomial bound for the number of maximal systems of imprimitivity of a finite transitive permutation group
- Well-posedness of backward stochastic partial differential equations with Lyapunov condition
- Free division rings of fractions of crossed products of groups with Conradian left-orders
- Strong uncountable cofinality for unitary groups of von Neumann algebras
- Irreducible holonomy groups and first integrals for holomorphic foliations
- Alexandroff topologies and monoid actions
Articles in the same Issue
- Frontmatter
- Approximating pointwise products of quasimodes
- On the group of a rational maximal bifix code
- Hörmander type multiplier theorems on bi-parameter anisotropic Hardy spaces
- Newton’s method for nonlinear stochastic wave equations
- On the classification of Schreier extensions of monoids with non-abelian kernel
- Smoothness filtration of the magnitude complex
- Varieties of nilpotent Lie superalgebras of dimension ≤ 5
- The Dual Baer Criterion for non-perfect rings
- Spectral property of the planar self-affine measures with three-element digit sets
- Spectral properties of certain Moran measures with consecutive and collinear digit sets
- Envelopes of circles and spacelike curves in the Lorentz–Minkowski 3-space
- A polynomial bound for the number of maximal systems of imprimitivity of a finite transitive permutation group
- Well-posedness of backward stochastic partial differential equations with Lyapunov condition
- Free division rings of fractions of crossed products of groups with Conradian left-orders
- Strong uncountable cofinality for unitary groups of von Neumann algebras
- Irreducible holonomy groups and first integrals for holomorphic foliations
- Alexandroff topologies and monoid actions