AN EXPLICIT FORMULA FOR LEBESGUE CONSTANTS ON VILENKIN GROUPS

Authors

  • Amil Pečenković University of Sarajevo, Department of Mathematics, 71000 Sarajevo, Zmaja od Bosne 33-35, Bosnia and Herzegovina

DOI:

https://doi.org/10.5644/SJM.22.01.09

Keywords:

Vilenkin group, Lebesgue constants

Abstract

We derive an explicit formula for Lebesgue constants on Vilenkin groups.

 

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References

G. N. Agaev, N. Ya. Vilenkin, G. M. Dzhafarli and A. I. Rubinshteĭn, Multiplicative systems of functions and harmonic analysis on zero-dimensional groups (in Russian), Elm, Baku, 1981.

I. Blahota, L. E. Persson and G. Tephnadze, Two-sided estimates of the Lebesgue constants with respect to Vilenkin systems and applications, Glasg. Math. J., 60 (2018), 17--34.

L. Fejér, Sur les singularités de la série de Fourier des fonctions continues, Ann. Sci. École Norm. Sup., 28 (1911), 63--104.

G. H. Hardy, Note on Lebesgue's constants in the theory of Fourier series, J. London Math. Soc., 17 (1942), 4--13.

E. Hewitt and K. A. Ross, Abstract harmonic analysis, vol. I, Springer-Verlag, Berlin, 1963.

Y. Katznelson, An introduction to harmonic analysis, Cambridge University Press, Cambridge, 2004.

A. Pečenković, On decomposition of the Dirichlet kernel on Vilenkin groups, Sarajevo J. Math., 18 (2022), 257--264.

E. M. Stein and R. Shakarchi, Fourier Analysis, Princeton University Press, New Jersey, 2003.

G. Szegő, Über the Lebesgueschen Konstanten bei den Fourierschen Reihen, Math. Z., 9 (1921), 163--166.

N. Ya. Vilenkin, On a class of complete orthonormal systems, Amer. Math. Soc. Transl., 28 (1963), 1--35.

A. Zygmund, Trigonometric series. Vol I, II, Cambridge University Press, Cambridge, 2002.

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Published

27.07.2026

How to Cite

Pečenković, A. (2026). AN EXPLICIT FORMULA FOR LEBESGUE CONSTANTS ON VILENKIN GROUPS. Sarajevo Journal of Mathematics, 22(01), 119–126. https://doi.org/10.5644/SJM.22.01.09

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