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Equidistribution of Continuous Functions Along Monotone Compact Covers Cover

Equidistribution of Continuous Functions Along Monotone Compact Covers

Open Access
|Aug 2023

References

  1. BERGELSON, V.—MOREIRA, J.: Van der Corput’s difference theorem: some modern developments, Indagationes Math. 27 (2016), 437–479.
  2. CIGLER, J.: The fundamental theorem of van der Corput on uniform distribution and its generalizations, Compositio Math. 16 (1964), 29–34.
  3. CONWAY, J. B.: A Course in Functional Analysis, Second Edition, Springer-Verlag, Berlin, 1990.
  4. DAVIS, H.: On the mean value of Haar measurable almost periodic functions, Duke Math. J. 34 (1967), 201–214.
  5. DALES, H. G.: Banach Algebras and Automatic Continuity,Oxford University Press, Oxford, 2000.
  6. DERIGHETTI, A.: Convolution Operators on Groups, Lecture Notes of the Unione Matematica Italiana Vol. 11, Springer, New York, 2011.
  7. DIXMIER, J.: Les C∗-Algèbres et Leurs Représentations,DeuxièmeÉdition,Éditions Jacques Gabay, Paris, 1996.
  8. ECKMANN, B.:Über monothetische Gruppen, Comment. Math. Helv. 16 (1943), 249–263.
  9. EDEKO, N.—KREIDLER, H.—NAGEL, R.: A dynamical proof of the van der Corput inequality, Dynam. Sys. Int. J. 2022. (published online)
  10. EYMARD, P.: L’algèbre de Fourier d’un groupe localement compact, Bull. Soc. Math. France 92 (1964), 181–236.
  11. FOLLAND, G. B.: A Course in Abstract Harmonic Analysis, CRC Press, Boca Raton, 1995.
  12. GEORGOPOULOS, P.—GRYLLAKIS, C.: Invariant measures for skew products and uniformly distributed sequences, Monatsh. Math. 167 (2012), 81–103.
  13. GEORGOPOULOS, P.—GRYLLAKIS, C.: Invariant measures for skew products and uniformly distributed sequences II, Monatsh. Math. 178 (2015), 191–220.
  14. GODEMENT, R.: Les fonctions de type positif et la théorie des groupes,Trans. Amer. Math. Soc. 63 (1948), 1–84.
  15. GREEN, B.—TAO, T.: The quantitative behaviour of polynomial orbits on nilmanifolds, Annals Math. 175 (2012), 465–540.
  16. GREEN, B.—TAO, T.: The Möbius function is strongly orthogonal to nilsequences, Ann of Math. 175 (2012), 541–566.
  17. HELMBERG, G.: Abstract theory of uniform distribution, Compositio Math. 16 (1964), 72–82.
  18. HERZ, C.: Harmonic synthesis for subgroups, Ann. Inst. Fourier (Grenoble) 23 (1973), 91–123.
  19. HEWITT, E.—ROSS, K. A.: Abstract Harmonic Analysis Vol. 1. Second Edition, Springer-Verlag, Berlin, 1979.
  20. HLAWKA, E.: Zur formalen Theorie der Gleichverteilung in kompakten Gruppen, Rend. Circ. Mat. Palermo 4 (1955), 33–47.
  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.
  22. KUIPERS, L.—NIEDERREITER, H.: Uniform Distribution of Sequences. Dover Publications, New York, 2006.
  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.
  24. LIMIC, V.—LIMIĆ, N.: Equidistribution and uniform distribution: a probabilist’s perspective, Probability Surveys 15 (2018), 131–155.
  25. VON NEUMANN, J.: Almost periodic functions in a group, I, Trans. Amer. Math. Soc. 36 (1934), 445–492.
  26. PATERSON, A.L.T.: Amenability.In:Mathematical Surveys Monographs, Vol. 29,Amer. Math. Soc., Providence RI, 1988.
  27. PARTHASARATHY, K. R.: Probability Measures on Metric Spaces.AcademicPress,New York, 1967.
  28. TAO, T.: Poincaré’s Legacies, Part I: Pages from Year Two of a Mathematical Blog. Amer. Math. Soc., Providence, RI, 2009.
  29. VAN DER CORPUT, J. G.: Diophantische Ungleichungen. I. Zur Gleichverteilung Modulo Eins,Acta Math. 56 (1931), 374–456.
  30. VEECH, W. A.: Some questions of uniform distribution, Ann. of Math. Soc. 94 (1971), no. 2, 125–138.
  31. VEECH, W. A.: Topological dynamics, Bull. Amer. Math. Soc. 83 (1977), no. 5, 775–830.
  32. WEYL, H.:Über die Gleichverteilung von Zahlen mod. Eins, Math. Ann. 77 (1916), 313–352.
  33. WILLARD, S.: General Topology, Reprint of the 1970 original [Addison-Wesley, Reading, MA]. Dover Publications, Inc., Mineola, NY, 2004.
DOI: https://doi.org/10.2478/udt-2023-0004 | Journal eISSN: 2309-5377 | Journal ISSN: 1336-913X
Language: English
Page range: 39 - 64
Submitted on: May 2, 2022
Accepted on: Feb 12, 2023
Published on: Aug 10, 2023
Published by: Slovak Academy of Sciences, Mathematical Institute
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2023 Mehdi Sangani Monfared, Yihan Zhu, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.