Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 20 (2025), 381 -- 388

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(C,2)(E,q) PRODUCT MEANS AND FOURIER-STIELTJES SERIES

Jaeman Kim

Abstract. In this paper, as a sequel to [3], we generalize Fejer's theorem on the determination of jumps of functions of bounded variation to Fourier-Stieltjes series in terms of (C,2)(E,q) product means.

2020 Mathematics Subject Classification: 42A24, 42A38.
Keywords: Fourier-Stieltjes series; (C,2)(E,q) product means.

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References

  1. L. Fejer, Uber die Bestimmung des Sprunges der Funktion aus ihrer Fourierreihe, J. Reine Angew Math. 142 (1913), 165-188. MR1580866. JFM 44.0483.01.

  2. G.H. Hardy, Divergent Series, Oxford Univ. Press, Oxford, 1949. MR0030620. Zbl 0032.05801.

  3. J. Kim, Determination of a jump by (E,q) means of Fourier-Stieltjes series, Publications de l’Institut Mathématique (Beograd) (N.S.) 113 (2023), 93-97. MR4599717. Zbl 1538.42006.

  4. K. Knopp, Ueber das Eulersche Summierungsverfahren, Math. Z. 15 (1922), 226-253. MR1544570. JFM 48.0232.01.

  5. F. Moricz, Fejer type theorems for Fourier-Stieltjes series, Analysis Mathematica, 30 (2004), 123-136. MR2075721. Zbl 1067.42002.

  6. A. Zygmund, Trigonometric Series, Vol. 1, Cambridge Univ. Press, Cambridge, 1959. MR0236587. Zbl 0085.05601.



Jaeman Kim
Department of Mathematics Education, Kangwon National University,
Chunchon 200-701, Kangwon-Do, Korea.
E-mail: jaeman64@kangwon.ac.kr

https://www.utgjiu.ro/math/sma