On almost even arithmetical functions via orthonormal systems on Vilenkin groups

• Autorzy: G. Gát
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1991-1992
• Tom: 60
• Numer: 2
• Strony: 105-123

Daty

wydano

1991

otrzymano

1990-05-24

poprawiono

1991-02-20

Twórcy

autor

G. Gát

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

Bibliografia

• [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 $L^p$-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).