Fuglede’s conjecture is false in 5 and higher dimensions
Open accessAbstract
We give an example of a set Ω ⊂ R 5 which is a finite union of unit cubes, such that L 2 (Ω) admits an orthonormal basis of exponentials { 1 |Ω| 1/2 e 2πiξ j •x : ξ j ∈ Λ} for some discrete set Λ ⊂ R 5 , but which does not tile R 5 by translations.This answers (one direction of) a conjecture of Fuglede [1] in the negative, at least in 5 and higher dimensions.
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Commuting self-adjoint partial differential operators and a group theoretic problem
Fuglede, B. (1974) · Journal of Functional Analysis · doi:10.1016/0022-1236(74)90072-x · Cited by 543 · see citing works
Fuglede’s conjecture for a union of two intervals
Łaba, I. (2001) · Proceedings of the American Mathematical Society · doi:10.1090/s0002-9939-01-06035-x · Cited by 141 · see citing works
The Spectral Set Conjecture and Multiplicative Properties of Roots of Polynomials
Łaba, I. (2002) · Journal of the London Mathematical Society · doi:10.1112/s0024610702003149 · Cited by 122 · see citing works
Keller’s cube-tiling conjecture is false in high dimensions
Lagarias, J. C., & Shor, P. W. (1992) · Bulletin of the American Mathematical Society · doi:10.1090/s0273-0979-1992-00318-x · Cited by 114 · see citing works
Spectral Sets and Factorizations of Finite Abelian Groups
Lagarias, J. C., & Wang, Y. (1997) · Journal of Functional Analysis · doi:10.1006/jfan.1996.3008 · Cited by 97 · see citing works
Orthonormal bases of exponentials for the n-cube
Lagarias, J. C., Reeds, J. A., & Wang, Y. (2000) · Duke Mathematical Journal · doi:10.1215/s0012-7094-00-10312-2 · Cited by 96 · see citing works
Convex bodies with a point of curvature do not have Fourier bases
Iosevich, A., Katz, N. H., & Tao, T. (2001) · American Journal of Mathematics · doi:10.1353/ajm.2001.0003 · Cited by 95 · see citing works
Self-citationNon-symmetric convex domains have no basis of exponentials
Kolountzakis, M. N. (2000) · Illinois Journal of Mathematics · doi:10.1215/ijm/1256060414 · Cited by 87 · see citing works
The Study of Translational Tiling with Fourier Analysis
Kolountzakis, M. N. (2004) · Applied and numerical harmonic analysis · doi:10.1007/978-0-8176-8172-2_7 · Cited by 73 · see citing works
Universal spectra, universal tiling sets and the spectral set conjecture
Pedersen, S., & Wang, Y. (2001) · MATHEMATICA SCANDINAVICA · doi:10.7146/math.scand.a-14325 · Cited by 66 · see citing works
Packing, Tiling, Orthogonality and Completeness
Kolountzakis, M. N. (2000) · Bulletin of the London Mathematical Society · doi:10.1112/s0024609300007281 · Cited by 50 · see citing works
Wavelets, tiling, and spectral sets
Wang, Y. (2002) · Duke Mathematical Journal · doi:10.1215/s0012-7094-02-11413-6 · Cited by 47 · see citing works
Universal Spectra and Tijdeman's Conjecture on Factorization of Cyclic Groups
Lagarias, J. C., & Szabo, S. (2001) · Journal of Fourier Analysis and Applications · doi:10.1007/s00041-001-0005-y · Cited by 34 · see citing works
Orthogonal harmonic analysis of fractal measures
Jørgensen, P. E. T., & Pedersen, S. (1998) · Electronic Research Announcements of the American Mathematical Society · doi:10.1090/s1079-6762-98-00044-4 · Cited by 27 · see citing works
Spectra of certain types of polynomials and tiling of integers with translates of finite sets
Konyagin, S. V., & Łaba, I. (2003) · Journal of Number Theory · doi:10.1016/j.jnt.2003.06.006 · Cited by 25 · see citing works
A class of non-convex polytopes that admit no orthonormal basis of exponentials
Kolountzakis, M. N., & Papadimitrakis, M. (2002) · Illinois Journal of Mathematics · doi:10.1215/ijm/1258138476 · Cited by 17 · see citing works
Fuglede conjecture holds for convex planar domainsPreprint
Iosevich, A., Katz, N. H., & Tao, T. (2001) · arXiv (Cornell University) · doi:10.48550/arxiv.math/0104087 · Cited by 15 · see citing works
Self-citationSpectral and Tiling properties of the Unit CubePreprint
Iosevich, A., & Pedersen, S. (2001) · arXiv (Cornell University) · doi:10.48550/arxiv.math/0104093 · Cited by 14 · see citing works
Tiling and spectral properties of near-cubic domains
Kolountzakis, M. N., & Łaba, I. (2004) · Studia Mathematica · doi:10.4064/sm160-3-6 · Cited by 10 · see citing works
Flagged first, then by citations
2 of the 21 references couldn’t be matched to a known paper.
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Carolan, J., Harrold, C., Sparrow, C., Martín-López, E., Russell, N. J., Silverstone, J. W., Shadbolt, P. J., Matsuda, N., Oguma, M., Itoh, M., et al. (2015) · Science · doi:10.1126/science.aab3642 · Cited by 1,093 · see citing works
Durt, T., Englert, B., Bengtsson, I., & Życzkowski, K. (2010) · International Journal of Quantum Information · doi:10.1142/s0219749910006502 · Cited by 715 · see citing works
A Concise Guide to Complex Hadamard Matrices
Tadej, W., & Życzkowski, K. (2006) · Open Systems & Information Dynamics · doi:10.1007/s11080-006-8220-2 · Cited by 263 · see citing works
Kolountzakis, M. N., & Matolcsi, M. (2006) · Forum Mathematicum · doi:10.1515/forum.2006.026 · Cited by 230 · see citing works
When does a Bernoulli convolution admit a spectrum?
Dai, X.-R. (2012) · Advances in Mathematics · doi:10.1016/j.aim.2012.06.026 · Cited by 197 · see citing works
On spectral N -Bernoulli measures
Dai, X.-R., He, X., & Lau, K. (2014) · Advances in Mathematics · doi:10.1016/j.aim.2014.03.026 · Cited by 178 · see citing works
Hadamard triples generate self-affine spectral measures
Dutkay, D. E., Haussermann, J., & Lai, C.-K. (2018) · Transactions of the American Mathematical Society · doi:10.1090/tran/7325 · Cited by 171 · see citing works
Spectral property of Cantor measures with consecutive digits
Dai, X.-R., He, X., & Lai, C. (2013) · Advances in Mathematics · doi:10.1016/j.aim.2013.04.016 · Cited by 170 · see citing works
Analysis of orthogonality and of orbits in affine iterated function systems
Dutkay, D. E., & Jørgensen, P. E. T. (2007) · Mathematische Zeitschrift · doi:10.1007/s00209-007-0104-9 · Cited by 163 · see citing works
On the spectra of a Cantor measure
Dutkay, D. E., Han, D., & Sun, Q. (2009) · Advances in Mathematics · doi:10.1016/j.aim.2008.12.007 · Cited by 156 · see citing works
Complex Hadamard matrices and the Spectral Set Conjecture
Kolountzakis, M. N., & Matolcsi, M. (2004) · RACO (Revistes Catalanes amb Accés Obert) (Consorci de Serveis Universitaris de Catalunya) · doi:10.48550/arxiv.math/0411512 · Cited by 147 · see citing works
Fourier frequencies in affine iterated function systems
Dutkay, D. E., & Jørgensen, P. E. T. (2007) · Journal of Functional Analysis · doi:10.1016/j.jfa.2007.03.002 · Cited by 145 · see citing works
Fuglede’s conjecture fails in dimension 4
Matolcsi, M. (2005) · Proceedings of the American Mathematical Society · doi:10.1090/s0002-9939-05-07874-3 · Cited by 144 · see citing works
A class of spectral Moran measures
An, L.-X., & He, X. (2013) · Journal of Functional Analysis · doi:10.1016/j.jfa.2013.08.031 · Cited by 139 · see citing works
Mutually unbiased bases and Hadamard matrices of order six
Bengtsson, I., Bruzda, W., Ericsson, Å., Larsson, J.-Å., Tadej, W., & Życzkowski, K. (2007) · Journal of Mathematical Physics · doi:10.1063/1.2716990 · Cited by 130 · see citing works
Constructing mutually unbiased bases in dimension six
BRIERLEY, S. D., & Weigert, S. (2009) · Physical Review A · doi:10.1103/physreva.79.052316 · Cited by 116 · see citing works
He, X., Lai, C., & Lau, K. (2012) · Applied and Computational Harmonic Analysis · doi:10.1016/j.acha.2012.05.003 · Cited by 101 · see citing works
The Fuglede conjecture for convex domains is true in all dimensions
Lev, N., & Matolcsi, M. (2022) · Acta Mathematica · doi:10.4310/acta.2022.v228.n2.a3 · Cited by 100 · see citing works
On spectral Cantor-Moran measures and a variant of Bourgain's sum of sine problem
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Spectrality of a class of infinite convolutions
An, L.-X., He, X., & Lau, K. (2015) · Advances in Mathematics · doi:10.1016/j.aim.2015.07.021 · Cited by 96 · see citing works
Sierpinski-type spectral self-similar measures
Deng, Q.-R., & Lau, K. (2015) · Journal of Functional Analysis · doi:10.1016/j.jfa.2015.06.013 · Cited by 95 · see citing works
Dai, X.-R. (2016) · Mathematische Annalen · doi:10.1007/s00208-016-1374-5 · Cited by 85 · see citing works
Spectra of Bernoulli convolutions and random convolutions
Fu, Y.-S., He, X., & Wen, Z. (2018) · Journal de Mathématiques Pures et Appliquées · doi:10.1016/j.matpur.2018.06.002 · Cited by 79 · see citing works
On Fuglede’s conjecture and the existence of universal spectra
Farkas, B., Matolcsi, M., & Móra, P. (2006) · Repository of the Academy's Library (Library of the Hungarian Academy of Sciences) · Cited by 77 · see citing works
Spectrality of self-affine Sierpinski-type measures on R2
Dai, X.-R., Fu, X., & Yan, Z.-H. (2020) · Applied and Computational Harmonic Analysis · doi:10.1016/j.acha.2019.12.001 · Cited by 71 · see citing works
A Multiplier-Free Generator for Polyphase Complete Complementary Codes
Das, S., Budisin, S., Majhi, S., Liu, Z., & Guan, Y. L. (2017) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2017.2780050 · Cited by 64 · see citing works
The Fuglede conjecture holds in ℤp× ℤp
Iosevich, A., Mayeli, A., & Pakianathan, J. (2017) · Analysis & PDE · doi:10.2140/apde.2017.10.757 · Cited by 60 · see citing works
Some properties of spectral measures
Łaba, I., & Wang, Y. (2005) · Applied and Computational Harmonic Analysis · doi:10.1016/j.acha.2005.03.003 · Cited by 60 · see citing works
Tiles with no spectra in dimension 4
Farkas, B., & Révész, S. G. (2006) · MATHEMATICA SCANDINAVICA · doi:10.7146/math.scand.a-14982 · Cited by 59 · see citing works
Properties and applications of the Kirkwood–Dirac distribution
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Fourier duality for fractal measures with affine scales
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Spectrality of infinite Bernoulli convolutions
An, L.-X., He, X., & Li, H. (2015) · Journal of Functional Analysis · doi:10.1016/j.jfa.2015.05.008 · Cited by 54 · see citing works
Multiple lattice tiles and Riesz bases of exponentials
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On Fourier frame of absolutely continuous measures
Lai, C. (2011) · Journal of Functional Analysis · doi:10.1016/j.jfa.2011.07.014 · Cited by 51 · see citing works
Fuglede’s spectral set conjecture for convex polytopes
Greenfeld, R., & Lev, N. (2017) · Analysis & PDE · doi:10.2140/apde.2017.10.1497 · Cited by 51 · see citing works
On the Fourier orthonormal bases of Cantor–Moran measures
He, L., & He, X. (2016) · Journal of Functional Analysis · doi:10.1016/j.jfa.2016.09.021 · Cited by 51 · see citing works
A Novel Class of Complete Complementary Codes and Their Applications for APU Matrices
Das, S., Majhi, S., & Liu, Z. (2018) · IEEE Signal Processing Letters · doi:10.1109/lsp.2018.2849656 · Cited by 51 · see citing works
Fourier series on fractals: a parallel with wavelet theory
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μM,D -Orthogonality and compatible pair
Li, J. (2006) · Journal of Functional Analysis · doi:10.1016/j.jfa.2006.10.003 · Cited by 50 · see citing works
Spectrality of Self-Similar Tiles
Fu, X., He, X., & Lau, K. (2015) · Constructive Approximation · doi:10.1007/s00365-015-9306-2 · Cited by 49 · see citing works
Spectrality and non-spectrality of the Riesz product measures with three elements in digit sets
An, L.-X., He, L., & He, X. (2018) · Journal of Functional Analysis · doi:10.1016/j.jfa.2018.10.017 · Cited by 46 · see citing works
Spectral measures with arbitrary Hausdorff dimensions
Dai, X.-R., & Sun, Q. (2015) · Journal of Functional Analysis · doi:10.1016/j.jfa.2015.01.005 · Cited by 46 · see citing works
Some reductions of the spectral set conjecture to integers
DUTKAY, D. E., & LAI, C. (2013) · Mathematical Proceedings of the Cambridge Philosophical Society · doi:10.1017/s0305004113000558 · Cited by 45 · see citing works
Orthogonal maximal abelian * -subalgebras of the 6×6 matrices
Beauchamp, K. A., & Nicoară, R. (2008) · Linear Algebra and its Applications · doi:10.1016/j.laa.2007.10.023 · Cited by 45 · see citing works
Orthogonal exponentials, translations, and Bohr completions
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Spectral measures generated by arbitrary and random convolutions
Dutkay, D. E., & Lai, C. (2016) · Journal de Mathématiques Pures et Appliquées · doi:10.1016/j.matpur.2016.06.003 · Cited by 42 · see citing works
Spectrality of infinite convolutions with three-element digit sets
Fu, Y.-S., & Wen, Z. (2017) · Monatshefte für Mathematik · doi:10.1007/s00605-017-1026-1 · Cited by 41 · see citing works
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Fuglede’s conjecture holds in $$\mathbb {Q}_{p}$$
Fan, A., Fan, S., Liao, L., & Shi, R. (2019) · Mathematische Annalen · doi:10.1007/s00208-019-01867-8 · Cited by 40 · see citing works
Tadej, W., & Życzkowski, K. (2008) · Linear Algebra and its Applications · doi:10.1016/j.laa.2008.02.036 · Cited by 39 · see citing works
Construction, classification and parametrization of complex Hadamard matricesPreprint
Szöllősi, F. (2011) · arXiv (Cornell University) · doi:10.48550/arxiv.1110.5590 · Cited by 39 · see citing works
Orthogonal Exponentials for Bernoulli Iterated Function Systems
Jørgensen, P. E. T., Kornelson, K., & Shuman, K. L. (2008) · Birkhäuser Boston eBooks · doi:10.1007/978-0-8176-4683-7_11 · Cited by 38 · see citing works
Mutually unbiased bases and semi-definite programming
Brierley, S., & Weigert, S. (2010) · Journal of Physics Conference Series · doi:10.1088/1742-6596/254/1/012008 · Cited by 37 · see citing works
The limited role of mutually unbiased product bases in dimension 6
McNulty, D., & Weigert, S. (2012) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/45/10/102001 · Cited by 37 · see citing works
Spectrality of the planar Sierpinski family
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Complex Hadamard matrices of order 6: a four-parameter familyPreprint
Szöllősi, F. (2010) · Cited by 35 · see citing works
Spectral property of self-affine measures on Rn
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An, L.-X., & Wang, C. (2020) · Journal of Functional Analysis · doi:10.1016/j.jfa.2020.108821 · Cited by 34 · see citing works
Periodicity of the spectrum in dimension one
Iosevich, A., & Kolountzakis, M. N. (2013) · Analysis & PDE · doi:10.2140/apde.2013.6.819 · Cited by 34 · see citing works
Exotic complex Hadamard matrices and their equivalence
Szöllősi, F. (2010) · Cryptography and Communications · doi:10.1007/s12095-010-0021-3 · Cited by 32 · see citing works
Periodicity and decidability of tilings of ℤ2
Bhattacharya, S. S. (2020) · American Journal of Mathematics · doi:10.1353/ajm.2020.0006 · Cited by 31 · see citing works
Weak convergence and spectrality of infinite convolutions
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Representations of quantum permutation algebras
Banica, T., Bichon, J., & Schlenker, J. (2009) · Journal of Functional Analysis · doi:10.1016/j.jfa.2009.04.013 · Cited by 30 · see citing works
Spectral structure of digit sets of self-similar tiles on ℝ¹
Lai, C., Lau, K., & Rao, H. (2013) · Transactions of the American Mathematical Society · doi:10.1090/s0002-9947-2013-05787-x · Cited by 29 · see citing works
Turán’s extremal problem on locally compact abelian groups
Révész, S. G. (2011) · Analysis Mathematica · doi:10.1007/s10476-011-0102-3 · Cited by 28 · see citing works
New Optimal $Z$-Complementary Code Sets Based on Generalized Paraunitary Matrices
Das, S., Parampalli, U., Majhi, S., Liu, Z., & Budisin, S. (2020) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2020.3021977 · Cited by 27 · see citing works
Chen, M., & Liu, J. (2018) · Journal of Functional Analysis · doi:10.1016/j.jfa.2018.11.012 · Cited by 26 · see citing works
Relating incompatibility, noncommutativity, uncertainty, and Kirkwood–Dirac nonclassicality
Bièvre, S. D. (2023) · Journal of Mathematical Physics · doi:10.1063/5.0110267 · Cited by 26 · see citing works
Quasiperiodic spectra and orthogonality for iterated function system measures
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Spectrality of generalized Sierpinski-type self-affine measures
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Compact open spectral sets in Qp
Fan, A., Fan, S., & Shi, R. (2016) · Journal of Functional Analysis · doi:10.1016/j.jfa.2016.08.021 · Cited by 25 · see citing works
Multi-tiling sets, Riesz bases, and sampling near the critical density in LCA groups
Cabrelli, C., Antezana, J., & Agora, E. (2015) · Conicet · Cited by 25 · see citing works
Spectrality of Moran-type self-similar measures on R
Deng, Q.-R., & Li, M. (2021) · Journal of Mathematical Analysis and Applications · doi:10.1016/j.jmaa.2021.125547 · Cited by 24 · see citing works
Tiling sets and spectral sets over finite fields
Aten, C., Ayachi, B., Bau, E., FitzPatrick, D., Iosevich, A., Liu, H., Lott, A., MacKinnon, I., Maimon, S., Nan, S., et al. (2016) · Journal of Functional Analysis · doi:10.1016/j.jfa.2016.10.018 · Cited by 24 · see citing works
On the discrete Fuglede and Pompeiu problems
Kiss, G., Romanos, D. M., Somlai, G., & Máté, V. (2019) · Repository of the Academy's Library (Library of the Hungarian Academy of Sciences) · Cited by 24 · see citing works
Spectrum is periodic for n-intervals
Bose, D., & Madan, S. (2010) · Journal of Functional Analysis · doi:10.1016/j.jfa.2010.09.011 · Cited by 23 · see citing works
Spectral theory of multiple intervals
Jørgensen, P. E. T., Pedersen, S., & Tian, F. (2014) · Transactions of the American Mathematical Society · doi:10.1090/s0002-9947-2014-06296-x · Cited by 23 · see citing works
A two-parameter family of complex Hadamard matrices of order 6 induced by hypocycloids
Szöllősi, F. (2009) · Proceedings of the American Mathematical Society · doi:10.1090/s0002-9939-09-10102-8 · Cited by 23 · see citing works
Fuglede’s conjecture fails in 4 dimensions over odd prime fields
Ferguson, S. J., & Sothanaphan, N. (2019) · Discrete Mathematics · doi:10.1016/j.disc.2019.04.026 · Cited by 23 · see citing works
Detecting entanglement can be more effective with inequivalent mutually unbiased bases
Hiesmayr, B. C., McNulty, D., Baek, S., Roy, S. S., Bae, J., & Chruściński, D. (2021) · New Journal of Physics · doi:10.1088/1367-2630/ac20ea · Cited by 22 · see citing works
On the discrete Fuglede and Pompeiu problems
Kiss, G., Malikiosis, R. D., Somlai, G., & Vizer, M. (2020) · Analysis & PDE · doi:10.2140/apde.2020.13.765 · Cited by 22 · see citing works
Unbiased bases (Hadamards) for six-level systems: Four ways from Fourier
Skinner, A. J., Newell, V. A., & Sánchez, R. D. (2009) · Journal of Mathematical Physics · doi:10.1063/1.3059166 · Cited by 22 · see citing works
Spectral measures and Cuntz algebras
Dutkay, D. E., & Jørgensen, P. E. T. (2012) · Mathematics of Computation · doi:10.1090/s0025-5718-2012-02589-0 · Cited by 21 · see citing works
Equi‐distributed property and spectral set conjecture on Zp2×Zp
Shi, R. (2020) · Journal of the London Mathematical Society · doi:10.1112/jlms.12346 · Cited by 21 · see citing works
Quantum groups and Hadamard matricesPreprint
Banica, T., & Nicoara, R. (2006) · arXiv (Cornell University) · doi:10.48550/arxiv.math/0610529 · Cited by 21 · see citing works
Momentum operators in two intervals: Spectra and phase transitionPreprint
Jørgensen, P. E. T., Pedersen, S., & Tian, F. (2012) · Cited by 21 · see citing works
Fourier Frames for Surface-Carried Measures
Iosevich, A., Lai, C., Liu, B., & Wyman, E. L. (2020) · International Mathematics Research Notices · doi:10.1093/imrn/rnz318 · Cited by 20 · see citing works
Fuglede’s Conjecture Holds for Cyclic Groups of Order pqrs
Kiss, G., Malikiosis, R. D., Somlai, G., & Vizer, M. (2022) · Journal of Fourier Analysis and Applications · doi:10.1007/s00041-022-09972-0 · Cited by 20 · see citing works
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Łaba, I., & Londner, I. (2022) · Inventiones mathematicae · doi:10.1007/s00222-022-01169-y · Cited by 20 · see citing works
Spectral Moran measures on R 2 *
Yan, Z.-H. (2022) · Nonlinearity · doi:10.1088/1361-6544/ac4a8a · Cited by 20 · see citing works
Jørgensen, P. E. T., Kornelson, K., & Shuman, K. L. (2012) · Numerical Functional Analysis and Optimization · doi:10.1080/01630563.2012.682127 · Cited by 20 · see citing works
On the structure of spectral and tiling subsets of cyclic groups
Malikiosis, R. D. (2022) · Forum of Mathematics Sigma · doi:10.1017/fms.2022.14 · Cited by 20 · see citing works
Jørgensen, P. E. T. (2018) · Regional conference series in mathematics · doi:10.1090/cbms/128 · Cited by 19 · see citing works
Product states and Schmidt rank of mutually unbiased bases in dimension six
Chen, L., & Yu, L. (2017) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/aa8f9e · Cited by 19 · see citing works
Spectrality of Sierpinski-type self-affine measures
Lu, Z.-Y., Dong, X., & Liu, Z.-S. (2021) · Journal of Functional Analysis · doi:10.1016/j.jfa.2021.109310 · Cited by 18 · see citing works
Spectral property of a class of Moran measures on R
Fu, Y.-S., & Wen, Z. (2015) · Journal of Mathematical Analysis and Applications · doi:10.1016/j.jmaa.2015.05.006 · Cited by 18 · see citing works
Riesz bases of exponentials for convex polytopes with symmetric faces
Pinos, A. D., & Lev, N. (2021) · Journal of the European Mathematical Society · doi:10.4171/jems/1158 · Cited by 18 · see citing works
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Li, J., & Wu, Z. (2022) · Nonlinearity · doi:10.1088/1361-6544/ac6b0c · Cited by 17 · see citing works
New perspectives on rhythmic canons and the spectral conjecture
Emmanuel Amiot, C. (2009) · Journal of Mathematics and Music · doi:10.1080/17459730903040709 · Cited by 17 · see citing works
- Authors
- Tao, T.
- Affiliations
- University of California, Los Angeles (US)
- Corresponding author
- Tao, Terence
- ORCID
- Tao, Terence
- Venue
- Mathematical Research Letters
- Publisher
- International Press of Boston
- Published
- 2004
- Volume
- 11
- Issue
- 2
- Pages
- 251-258
- ISSN
- 1073-2780 (ISSN-L)
- 1945-001X
- OpenAlex
- W2009600348
- Cited by
- 392
- References
- 21
- Citations by year
- 2026: 17 · 2025: 28 · 2024: 26 · 2023: 33 · 2022: 30 · 2021: 27 · 2020: 22 · 2019: 23 · 2018: 20 · 2017: 18 · 2016: 17 · 2015: 19 · 2014: 11 · 2013: 20 · 2012: 19
- FWCI
- 12.66
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Mathematical Research Letters (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Mathematics › Applied Mathematics › Mathematical Analysis and Transform Methods
- Physical Sciences › Mathematics › Mathematical Physics › Spectral Theory in Mathematical Physics
- Physical Sciences › Mathematics › Algebra and Number Theory › Analytic Number Theory Research
- Keywords
- Fuglede conjecture, counterexample, unit cube, exponential bases, discrete sets, extra dimensions, L2 spaces
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