About Characters and the Dirichlet Kernel on Vilenkin Groups

Authors

  • Medo Pepić Department of Mathematics, University of Sarajevo, Sarajevo, Bosnia and Herzegovina

DOI:

https://doi.org/10.5644/SJM.04.1.10

Keywords:

Vilenkin group, the character of the group, Dirichlet kernel on Vilenkin Group, Fourier-Vilenkin series

Abstract

In this paper we study properties of characters and the Dirichlet kernel on Vilenkin groups which are of key importance for analyzing convergence, integrability and summability of Fourier-Vilenkin series.

 

2000 Mathematics Subject Classification. 42C10, 43A40

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References

G. N. Agaev, N. Ya. Vilenkin, G. M. Dˇzafarli and A. I. Rubinˇstein, Multiplikativnye sistemy funkci˘ı i garmonicheskii˘ı anaiz na multiplikativnyh gruppah, Elm, Baku, 1981.

B. Aubertin and J. J. F. Fournier, An integrability theorem for unbounded Vilenkin systems, Anal. Math., 23 (1997), 159–187.

S. Fridli and F. Schipp, On the everywhere divergence of the Vilenkin-Fourier series, Acta Math. Sci., (Szeged), 48 (1985), 155–162.

E. Hewitt and K. A. Ross, Abstract harmonic analysis, Vol. I, Springer-Verlag, Berlin, 1963; translated in Nauka, Moskva, 1975.

C. W. Onneweer and D. Waterman, Uniform convergence of Fourier series on groups, I, Michigan Math. J., 18 (1971), 265–273.

Zbl pre 01310541 Pepi´c Medo, Integrability and summability of Vilenkin series, (Serbian, English summary) (doktorate disertation).

N. Tanovi´c-Miller, Integrability and $L^{1}$ convergence classes for unbounded Vilenkin systems, Acta Math. Sci., (Szeged), 69 (2003), 687–732.

N. Ya. Vilenkin, On a class of complete orhtonormal systems, Izv. Akad. Nauk. SSSR Ser. Math. 11 (1947), 363–400; translated in Amer. Math. Soc. Transl. 28 (1963), 1–35.

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Published

11.06.2024

How to Cite

Pepić, M. (2024). About Characters and the Dirichlet Kernel on Vilenkin Groups. Sarajevo Journal of Mathematics, 4(1), 109–123. https://doi.org/10.5644/SJM.04.1.10

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Articles