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On the absolute Hausdorff summability factors of a Fourier series

Published online by Cambridge University Press:  24 October 2008

N. Tripathy
N. Tripathy
Affiliation:
Ravenshaw College, Cuttack, India
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Extract

Let be a given infinite series with the sequence of partial sums {sn}. Then the sequence-to-sequence Hausdorff transformation of the sequence {sn} is given by

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 66 , Issue 2 , September 1969 , pp. 355 - 363
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

REFERENCES

(1)Bosanquet, L. S.The absolute Cesàro summability of a Fourier Series. Proc. Lond. Math. Soc. 41 (1936), 517–529.Google Scholar
(2)Cheng, M. T.Summability factors of Fourier Series. Duke Math. J. 15 (1948), 17–27.Google Scholar
(3)Hardy, G. H.Divergent series (Oxford, 1949).Google Scholar
(4)Hausdorff, F.Summationsmethoden und momentfolgen I. Math. Z. 9 (1921), 74–109.Google Scholar
(5)Knopp, K. and Lorentz, G. G.Beitrage zur absoluten Limitierung. Arch. Math 2 (1949/1950), 10–16.Google Scholar
(6)Kuttner, B.On the ‘second theorem of consistency’ for Riesz summability (II). J. London Math Soc. 27 (1952), 207–217.CrossRefGoogle Scholar
(7)Ramanujan, M. S.On Hausdorff and quasi-Hausdorff methods of summability. Quart. J. Math. Oxford Ser. 8 (1957), 197–213.Google Scholar
(8)Tbipathy, N.On the absolute Hausdorff summability of Fourier series. J. London Math. Soc. 44 (1969), 15–25.CrossRefGoogle Scholar
(9)Zygmund, A.Trigonometric series (Cambridge, 1959).Google Scholar