Equidistribution of Continuous Functions Along Monotone Compact Covers

[1] BERGELSON, V.—MOREIRA, J.: Van der Corput’s difference theorem: some modern developments, Indagationes Math. 27 (2016), 437–479. Search in Google Scholar

[2] CIGLER, J.: The fundamental theorem of van der Corput on uniform distribution and its generalizations, Compositio Math. 16 (1964), 29–34. Search in Google Scholar

[3] CONWAY, J. B.: A Course in Functional Analysis, Second Edition, Springer-Verlag, Berlin, 1990. Search in Google Scholar

[4] DAVIS, H.: On the mean value of Haar measurable almost periodic functions, Duke Math. J. 34 (1967), 201–214. Search in Google Scholar

[5] DALES, H. G.: Banach Algebras and Automatic Continuity,Oxford University Press, Oxford, 2000. Search in Google Scholar

[6] DERIGHETTI, A.: Convolution Operators on Groups, Lecture Notes of the Unione Matematica Italiana Vol. 11, Springer, New York, 2011. Search in Google Scholar

[7] DIXMIER, J.: Les C^∗-Algèbres et Leurs Représentations,DeuxièmeÉdition,Éditions Jacques Gabay, Paris, 1996. Search in Google Scholar

[8] ECKMANN, B.:Über monothetische Gruppen, Comment. Math. Helv. 16 (1943), 249–263. Search in Google Scholar

[9] EDEKO, N.—KREIDLER, H.—NAGEL, R.: A dynamical proof of the van der Corput inequality, Dynam. Sys. Int. J. 2022. (published online) Search in Google Scholar

[10] EYMARD, P.: L’algèbre de Fourier d’un groupe localement compact, Bull. Soc. Math. France 92 (1964), 181–236. Search in Google Scholar

[11] FOLLAND, G. B.: A Course in Abstract Harmonic Analysis, CRC Press, Boca Raton, 1995. Search in Google Scholar

[12] GEORGOPOULOS, P.—GRYLLAKIS, C.: Invariant measures for skew products and uniformly distributed sequences, Monatsh. Math. 167 (2012), 81–103. Search in Google Scholar

[13] GEORGOPOULOS, P.—GRYLLAKIS, C.: Invariant measures for skew products and uniformly distributed sequences II, Monatsh. Math. 178 (2015), 191–220. Search in Google Scholar

[14] GODEMENT, R.: Les fonctions de type positif et la théorie des groupes,Trans. Amer. Math. Soc. 63 (1948), 1–84. Search in Google Scholar

[15] GREEN, B.—TAO, T.: The quantitative behaviour of polynomial orbits on nilmanifolds, Annals Math. 175 (2012), 465–540. Search in Google Scholar

[16] GREEN, B.—TAO, T.: The Möbius function is strongly orthogonal to nilsequences, Ann of Math. 175 (2012), 541–566. Search in Google Scholar

[17] HELMBERG, G.: Abstract theory of uniform distribution, Compositio Math. 16 (1964), 72–82. Search in Google Scholar

[18] HERZ, C.: Harmonic synthesis for subgroups, Ann. Inst. Fourier (Grenoble) 23 (1973), 91–123. Search in Google Scholar

[19] HEWITT, E.—ROSS, K. A.: Abstract Harmonic Analysis Vol. 1. Second Edition, Springer-Verlag, Berlin, 1979. Search in Google Scholar

[20] HLAWKA, E.: Zur formalen Theorie der Gleichverteilung in kompakten Gruppen, Rend. Circ. Mat. Palermo 4 (1955), 33–47. Search in Google Scholar

[21] KANIUTH, E.—LAU, A. T.-M.: Fourier and Fourier-Stieltjes Algebras on Locally Compact Groups. Mathematical Surveys and Monographs. Vol. 231. Amer. Math. Soc. Providence, 2018. Search in Google Scholar

[22] KUIPERS, L.—NIEDERREITER, H.: Uniform Distribution of Sequences. Dover Publications, New York, 2006. Search in Google Scholar

[23] LEIBMAN, A.: Pointwise convergence of ergodic averages for polynomial sequences of translations on a nilmanifold, Ergodic Theory Dynam. Systems 25 (2005), no. 1, 201–213. Search in Google Scholar

[24] LIMIC, V.—LIMIĆ, N.: Equidistribution and uniform distribution: a probabilist’s perspective, Probability Surveys 15 (2018), 131–155. Search in Google Scholar

[25] VON NEUMANN, J.: Almost periodic functions in a group, I, Trans. Amer. Math. Soc. 36 (1934), 445–492. Search in Google Scholar

[26] PATERSON, A.L.T.: Amenability.In:Mathematical Surveys Monographs, Vol. 29,Amer. Math. Soc., Providence RI, 1988. Search in Google Scholar

[27] PARTHASARATHY, K. R.: Probability Measures on Metric Spaces.AcademicPress,New York, 1967. Search in Google Scholar

[28] TAO, T.: Poincaré’s Legacies, Part I: Pages from Year Two of a Mathematical Blog. Amer. Math. Soc., Providence, RI, 2009. Search in Google Scholar

[29] VAN DER CORPUT, J. G.: Diophantische Ungleichungen. I. Zur Gleichverteilung Modulo Eins,Acta Math. 56 (1931), 374–456. Search in Google Scholar

[30] VEECH, W. A.: Some questions of uniform distribution, Ann. of Math. Soc. 94 (1971), no. 2, 125–138. Search in Google Scholar

[31] VEECH, W. A.: Topological dynamics, Bull. Amer. Math. Soc. 83 (1977), no. 5, 775–830. Search in Google Scholar

[32] WEYL, H.:Über die Gleichverteilung von Zahlen mod. Eins, Math. Ann. 77 (1916), 313–352. Search in Google Scholar

[33] WILLARD, S.: General Topology, Reprint of the 1970 original [Addison-Wesley, Reading, MA]. Dover Publications, Inc., Mineola, NY, 2004. Search in Google Scholar