On almost even arithmetical functions via orthonormal systems on Vilenkin groups

G. Gát

Acta Arithmetica (1991)

  • Volume: 60, Issue: 2, page 105-123
  • ISSN: 0065-1036

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G. Gát. "On almost even arithmetical functions via orthonormal systems on Vilenkin groups." Acta Arithmetica 60.2 (1991): 105-123. <http://eudml.org/doc/206428>.

@article{G1991,
author = {G. Gát},
journal = {Acta Arithmetica},
keywords = {almost even arithmetical functions; harmonic analysis on Vilenkin groups; Vilenkin-Fourier series; modulus of continuity},
language = {eng},
number = {2},
pages = {105-123},
title = {On almost even arithmetical functions via orthonormal systems on Vilenkin groups},
url = {http://eudml.org/doc/206428},
volume = {60},
year = {1991},
}

TY - JOUR
AU - G. Gát
TI - On almost even arithmetical functions via orthonormal systems on Vilenkin groups
JO - Acta Arithmetica
PY - 1991
VL - 60
IS - 2
SP - 105
EP - 123
LA - eng
KW - almost even arithmetical functions; harmonic analysis on Vilenkin groups; Vilenkin-Fourier series; modulus of continuity
UR - http://eudml.org/doc/206428
ER -

References

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  1. [1] G. H. Agaev, N. Ya. Vilenkin, G. M. Dzhafarli and A. I. Rubinshteĭ, Multiplicative Systems of Functions and Harmonic Analysis on 0-dimensional Groups, Izd. 'ELM', Baku 1981 (in Russian). 
  2. [2] E. Cohen, A class of arithmetical functions, Proc. Nat. Acad. Sci. U.S.A. 41 (1955), 939-944. Zbl0066.29203
  3. [3] S. Fridli, On the modulus of continuity with respect to functions defined on Vilenkin groups, Acta Math. Acad. Sci. Hungar. 45 (3-4) (1985), 393-396. Zbl0569.43006
  4. [4] G. Gát, Orthonormal systems on Vilenkin groups, Acta Math. Acad. Sci. Hungar., to appear. Zbl0753.11027
  5. [5] G. Gát, On approximation of limit periodic arithmetical functions, Period. Math. Hungar., submitted. 
  6. [6] J. Gosselin, Almost everywhere convergence on Vilenkin-Fourier series, Trans. Amer. Math. Soc. 186 (1973), 345-370. Zbl0281.43007
  7. [7] A. Hildebrand, Über die punktweise Konvergenz von Ramanujan-Entwicklungen zahlentheoretischer Funktionen, Acta Arith. 44 (1984), 109-145. 
  8. [8] A. Hildebrand, W. Schwarz and J. Spilker, Still another proof of Parseval's equation for almost even arithmetical functions, Aequationes Math. 35 (1988), 132-139. Zbl0661.10065
  9. [9] J. Knopfmacher, Fourier analysis of arithmetical functions, Ann. Mat. Pura Appl. 109 (1976), 177-201. Zbl0337.10033
  10. [10] J. Knopfmacher, Abstract Analytic Number Theory, North Holland, Amsterdam 1975. Zbl0322.10001
  11. [11] A. I. Rubinshteĭ, On the modulus of continuity of functions defined on 0-dimensional groups, Mat. Zametki 23 (1978), 379-388 (in Russian). 
  12. [12] F. Schipp, On L p -norm convergence of series with respect to product systems, Anal. Math. 2 (1978), 49-64. 
  13. [13] F. Schipp, Pointwise convergence of expansions with respect to certain product systems, Anal. Math., 65-76. Zbl0343.42009
  14. [14] F. Schipp, W. R. Wade, P. Simon and J. Pál, Walsh Series. An Introduction to Dyadic Harmonic Analysis, Akadémiai Kiadó, Budapest, and Adam Hilger, Bristol and New York 1990. 
  15. [15] W. Schwarz und J. Spilker, Eine Anwendung des Approximationssatzes von Weierstrass-Stone auf Ramanujan-Summen, Nieuw Arch. Wisk. (3) 19 (1971), 198-209. 
  16. [16] W. Schwarz und J. Spilker, Mean values and Ramanujan expansions of almost even arithmetical functions, in: Topics in Number Theory, Colloq. Math. Soc. J. Bolyai 13, North-Holland, Amsterdam 1976, 315-357. 
  17. [17] P. Simon, On the divergence of Vilenkin-Fourier series, Acta Math. Hungar. 41 (3-4) (1983), 359-370. Zbl0522.42021
  18. [18] N. Ya. Vilenkin, On a class of complete orthonormal systems, Izv. Akad. Nauk SSSR Ser. Mat. 11 (1947), 363-400; English transl: Amer. Math. Soc. Transl. 28 (1963), 1-35. Zbl0036.35601
  19. [19] Zh. H. Zhantlesov, On absolute convergence of Fourier series with respect to multiplicative systems, Izv. Akad. Nauk Kazakh. SSR Ser. Fiz.-Mat. 3 (1986), 14-17 (in Russian). Zbl0609.43002

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