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Title

On almost even arithmetical functions via orthonormal systems on Vilenkin groups

Authors 1

Affiliations

  1. Department of Mathematics, Bessenyei College, P.O. Box 166, H-4401 Nyiregyháza, Hungary

Bibliography

  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. E. Cohen, A class of arithmetical functions, Proc. Nat. Acad. Sci. U.S.A. 41 (1955), 939-944.
  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.
  4. G. Gát, Orthonormal systems on Vilenkin groups, Acta Math. Acad. Sci. Hungar., to appear.
  5. G. Gát, On approximation of limit periodic arithmetical functions, Period. Math. Hungar., submitted.
  6. J. Gosselin, Almost everywhere convergence on Vilenkin-Fourier series, Trans. Amer. Math. Soc. 186 (1973), 345-370.
  7. A. Hildebrand, Über die punktweise Konvergenz von Ramanujan-Entwicklungen zahlentheoretischer Funktionen, Acta Arith. 44 (1984), 109-145.
  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.
  9. J. Knopfmacher, Fourier analysis of arithmetical functions, Ann. Mat. Pura Appl. 109 (1976), 177-201.
  10. J. Knopfmacher, Abstract Analytic Number Theory, North Holland, Amsterdam 1975.
  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. F. Schipp, On Lp-norm convergence of series with respect to product systems, Anal. Math. 2 (1978), 49-64.
  13. F. Schipp, Pointwise convergence of expansions with respect to certain product systems, Anal. Math., 65-76.
  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. W. Schwarz und J. Spilker, Eine Anwendung des Approximationssatzes von Weierstrass-Stone auf Ramanujan-Summen, Nieuw Arch. Wisk. (3) 19 (1971), 198-209.
  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. P. Simon, On the divergence of Vilenkin-Fourier series, Acta Math. Hungar. 41 (3-4) (1983), 359-370.
  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.
  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).
Acta Arithmetica
1991-1992/60/2
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Pages:
105-123
Main language of publication
English
Received
1990-05-24
Accepted
1991-02-20
Published
1991
Exact and natural sciences