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Our goal is to provide simple and practical algorithms in higher-order Fourier analysis which are based on spectral decompositions of operators.
H. Lebesgue. Sur la représentation trigonométrique approchée des fonctions satisfaisant à une condition de Lipschitz , Bull. Soc. Math. France 38
1910
Earlier work this paper cites.
N. R. Goodman, Statistical Analysis Based on a Certain Multivariate Complex Gaussian Distribution (An Introduction) , Ann. Math. Statist. 34 (1963), 152–177
1963
Earlier work this paper cites.
N. Bourbaki, Elements of mathematics. General topology. Part 1. Hermann, Paris; Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont. 1966
1966
Earlier work this paper cites.
Srinivasacharyulu, K. Variétés Différentielles et analytiques by N. Bourbaki. Hermann, Paris, 1967. 97 pages. , Canad. Math. Bull., 11
1968
Earlier work this paper cites.
E. Szemerédi, On sets of integers containing no k k elements in arithmetic progression , Acta Arith. 27
1975
Earlier work this paper cites.
H. Furstenberg, Ergodic behavior of diagonal measures and a theorem of Szemerédi on arithmetic progressions , J. Analyse Math. 31
1977
Earlier work this paper cites.
E. Szemerédi, Regular partitions of graphs , Problèmes combinatoires et théorie des graphes (Colloq. Internat. CNRS, Univ. Orsay, Orsay, 1976), pp. 399–401 Colloq. Internat. CNRS, 260
1978
Earlier work this paper cites.
M. P. do Carmo, Geometria riemanniana.[Riemannian geometry] , Projeto Euclides, 10 [Euclid Project], Instituto de Matemática Pura e Aplicada, Rio de Janeiro, 1979. ix+238 pp
1979
Earlier work this paper cites.
N. I. Akhiezer, I.M. Glazman, Theory of linear operators in Hilbert space. Vol. I. , translated from the third Russian edition by E. R. Dawson. Translation edited by W. N. Everitt Monogr. Stud. Math., 9 Pitman (Advanced Publishing Program), Boston, Mass.-London, 1981. xxxii+312 pp
1981
Earlier work this paper cites.
B. I. Golubov, Multiple series and Fourier integrals. (Russian) Mathematical analysis, Vol. 19, pp. 3–54, 232 Itogi Nauki i Tekhniki [Progress in Science and Technology] Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1982
1982
Earlier work this paper cites.
A. M. Frieze, R. Kannan, Quick Approximation to Matrices and Applications , Combinatorica 19
1999
Earlier work this paper cites.
A. M. Frieze, R. Kannan, A Simple Algorithm for Constructing Szemerédi’s Regularity Partition , Electron. J. Combin., 6
1999
Earlier work this paper cites.
N. Alon, E. Fischer, M. Krivelevich, M. Szegedy, Efficient testing of large graphs , Combinatorica 20
2000
Earlier work this paper cites.
W. T. Gowers, A new proof of Szemerédi’s theorem , Geom. Funct. Anal., 11
2001
Earlier work this paper cites.
2002
Earlier work this paper cites.
S. Aaronson, Algorithms for Boolean Function Query Properties , SIAM J. Comput. 32
2003
Earlier work this paper cites.
B. Host, B. Kra, Nonconventional ergodic averages and nilmanifolds , Ann. of Math. (2) 161
2005
Earlier work this paper cites.
V. Rödl, B. Nagle, J. Skokan, M. Schacht, Y. Kohayakawa, The hypergraph regularity method and its applications , Proc. Natl. Acad. Sci. USA. (2005) Jun 7;102
2005
Earlier work this paper cites.
L. N. Trefethen, M. Embree, Spectra and pseudospectra . The behavior of nonnormal matrices and operators Princeton University Press, Princeton, NJ, 2005. xviii+606 pp
2005
Earlier work this paper cites.
T. Tao, A quantitative ergodic theory proof of Szemerédi’s theorem , Electron. J. Combin. 13
2006
Earlier work this paper cites.
W. T. Gowers, Hypergraph regularity and the multidimensional Szemerédi theorem ,Ann. of Math. (2) 166
2007
Earlier work this paper cites.
T. Ziegler, Universal Characteristic Factors and Furstenberg Averages , J. Amer. Math. Soc. 20
2007
Earlier work this paper cites.
B. Green, T. Sanders, Boolean Functions with small Spectral Norm , Geom. Funct. Anal. 18
2008
Earlier work this paper cites.
B. Green, T. Tao, An inverse theorem for the Gowers U 3 U^{3} -norm , Proc. Edinburgh Math. Soc. (1) 51
2008
Cited alongside, same era.
B. Green, T. Tao, The primes contain arbitrarily long arithmetic progressions , Ann. of Math. (2) 167
2008
Cited alongside, same era.
B. Host, B. Kra, Parallelepipeds, nilpotent groups, and Gowers norms , Bull. Soc. Math. France 136
2008
Cited alongside, same era.
A. Gut, An Intermediate Course in Probability , Second edition, Springer Texts Statist. Springer, New York, 2009. xvi+303 pp
2009
Cited alongside, same era.
B. Szegedy, Higher order fourier analysis as an algebraic theory I , (2009), arXiv:0903.0897
2009
Cited alongside, same era.
J. M. Lee, Introduction to smooth manifolds, Second edition , Grad. Texts in Math., 218 Springer, New York, 2013. xvi+708 pp
2013
Later among the works it cites.
M. Tulsiani, J. Wolf, Quadratic Goldreich–Levin Theorems , SIAM J. Comput. 43
2014
Later among the works it cites.
P. Candela, Notes on nilspaces: algebraic aspects , Discrete Anal. 2017, Paper No. 15, 59 pp
2017
Later among the works it cites.
P. Candela, Notes on compact nilspaces , Discrete Anal. 2017, Paper No. 16, 57 pp
2017
Later among the works it cites.
W. T. Gowers, Generalizations of Fourier analysis, and how to apply them , Bull. Amer. Math. Soc. (N.S.) 54
2017
Later among the works it cites.
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2009
Cited alongside, same era.
L. Trevisan, Additive combinatorics and theoretical computer science , ACM SIGACT News (2) 40
2009
Cited alongside, same era.
O. A. Camarena, B. Szegedy, Nilspaces, nilmanifolds and their morphisms , (2010), arXiv:1009.3825
2010
Cited alongside, same era.
W. T. Gowers, Decompositions, approximate structure, transference, and the Hahn-Banach theorem , Bull. Lond. Math. Soc. 42
2010
Cited alongside, same era.
2010
Cited alongside, same era.
B. Green, T. Tao, An arithmetic regularity lemma, an associated counting lemma, and applications , in An Irregular Mind, Bolyai Soc. Math. Stud. 21, János Bolyai Mathematical Society, Budapest, 2010, pp. 261–334
2010
Cited alongside, same era.
I.D. Morris, A rapidly-converging lower bound for the joint spectral radius via multiplicative ergodic theory , Adv. Math. 225
2010
Cited alongside, same era.
2018
Later among the works it cites.
R. Vershynin, High-Dimensional Probability: An Introduction with Applications in Data Science , Camb. Ser. Stat. Probab. Math., 47 Cambridge University Press, Cambridge, 2018. xiv+284 pp
2018
Later among the works it cites.
Ş. Cobzaş, R. Miculescu, A. Nicolae, Lipschitz functions , Lecture Notes in Math., 2241 Springer, Cham, 2019. xiv+591 pp
2019
Later among the works it cites.
Y. Gutman, F. Manners, P. P. Varjú, The structure theory of nilspaces II: Representation as nilmanifolds , Trans. Amer. Math. Soc. 371
2019
Later among the works it cites.
H. Hatami, P. Hatami, S. Lovett, Higher-order Fourier analysis and applications , Found. Trends Theor. Comput. Sci. 13
2019
Later among the works it cites.
P. Candela, D. Gonzalez-Sanchez, B. Szegedy, On nilspace systems and their morphisms , Ergodic Theory Dynam. Systems 40
2020
Later among the works it cites.
2020
Later among the works it cites.
Y. Gutman, F. Manners, P. P. Varjú, The structure theory of nilspaces I , J. Anal. Math. 140
2020
Later among the works it cites.
Y. Gutman, F. Manners, P. P. Varjú, The structure theory of nilspaces III: Inverse limit representations and topological dynamics , Adv. Math. 365
2020
Later among the works it cites.
P. Candela, B. Szegedy, Regularity and inverse theorems for uniformity norms on compact abelian groups and nilmanifolds , J. Reine Angew. Math. 789
2022
Later among the works it cites.
P. Candela, D. Gonzalez-Sanchez, B. Szegedy, On higher-order Fourier analysis in characteristic p p , Ergodic Theory Dynam. Systems 43
2023
Later among the works it cites.
2023
Later among the works it cites.
P. Candela, B. Szegedy, Nilspace Factors for General Uniformity Seminorms, Cubic Exchangeability and Limits , Mem. Amer. Math. Soc. 287
2023
Later among the works it cites.
A. Jamneshan, T. Tao, The inverse theorem for the U 3 U^{3} Gowers uniformity norm on arbitrary finite abelian groups: Fourier-analytic and ergodic approaches , Discrete Anal. 2023, Paper No. 11, 48 pp
2023
Later among the works it cites.
2023
Later among the works it cites.
D. Kim, A. Li, J. Tidor, Cubic Goldreich-Levin , Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), 4846–4892
2023
Later among the works it cites.
L. Milićević, An inverse theorem for certain directional Gowers uniformity norms , Publ. Inst. Math. (Beograd) (N.S.) 113(127)
2023
Later among the works it cites.