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On the summability |R, log ω, 1| of Fourier series and an associated series

Published online by Cambridge University Press:  24 October 2008

R. Mohanty  and
B. K. Ray
R. Mohanty
Affiliation:
Ravenshaw College, Cuttack-3, India
B. K. Ray
Affiliation:
Ravenshaw College, Cuttack-3, India
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Extract

1. Definition. Let λ ≡ λ(ω) be continuous, differentiable and monotonic increasing in (0, ∞) and let it tend to infinity as ω → ∞. A series is summable |R, λ, r|, where r > 0, if

where A is a fixed positive number(3).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 3 , July 1967 , pp. 721 - 726
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

REFERENCES

(1)Bosanquet, L. S.Note on the absolute summability (C) of a Fourier series. J. London Math. Soc. 11 (1936), 11–15.CrossRefGoogle Scholar
(2)Izumi, S.Notes on Fourier Analysis (viii): Local properties of Fourier series. Tôhoku. Math. J. 1 (1950), 136–143.Google Scholar
(3)Mohanty, R.On the absolute Riesz summability of a Fourier series and its allied series. Proc. London Math. Soc. (2), 52 (1951), 295–320.Google Scholar
(4)Mohanty, R.On the summability |R, log ω, 1| of a Fourier series. J. London Math. Soc. 25 (1950), 67–72.CrossRefGoogle Scholar
(5)Mohanty, R. and Mahapatra, S.On the absolute logarithmic summability of a Fourier series and its differentiated Fourier series. Proc. American Math. Soc. 7 (1956), 254–259.CrossRefGoogle Scholar
(6)Mohanty, R. and Mahapatra, S.On the absolute logarithmic summability of a Fourier series. Math. Z. 65 (1956), 207–213.CrossRefGoogle Scholar