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On the summability |N, pn| of a Fourier series at a point

Published online by Cambridge University Press:  24 October 2008

H. P. Dikshit
H. P. Dikshit
Affiliation:
University of Allahabad, India
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Extract

Let ∑an be a given infinite series and {sn} the sequence of its partial sums. Let {pn} be a sequence of constants, real or complex, and let us write

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 65 , Issue 2 , March 1969 , pp. 495 - 506
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

REFERENCES

(1)Astrachan, Max.Studies in the summability of Fourier series by Nörlund means. Duke Math. J. 2 (1936), 543–568.CrossRefGoogle Scholar
(2)Bosanquet, L. S.The absolute Cesàro summability of a Fourier series. Proc. London Math. Soc. 41 (1936), 517–528.CrossRefGoogle Scholar
(3)Dikshit, H. P.On the absolute Nörlund summability of a Fourier series. Proc. Japan Acad. 40 (1964), 813–817.Google Scholar
(4)Dikshit, H. P.Absolute summability of Fourier series by Nörlund means. Math. Z. 102 (1967), 166–170.CrossRefGoogle Scholar
(5)Dikshit, H. P.On the absolute Nörlund summability of a Fourier series, I. Riv. Mat. Univ. Parma 7 (1966), 171–176.Google Scholar
(6)Hardy, G. H.Divergent Series (Oxford, 1949).Google Scholar
(7)McFadden, L.Absolute Nörlund summability. Duke Math. J. 9 (1942), 168–207.CrossRefGoogle Scholar
(8)Mears, F. M.Some multiplication theorems for the Nörlund means. Bull. Amer. Math. Soc. 41 (1935), 875–880.CrossRefGoogle Scholar
(9)Nörlund, N. E.Sur une application des fonctions permutables. Lunds Universitets Arsshrift (2), 16 (1919), No. 3.Google Scholar
(10)Pati, T.On the absolute Nörlund summability of a Fourier series. J. London Math. Soc. 34 (1959), 153–160; addendum: J. London Math. Soc. 37 (1962), 256.CrossRefGoogle Scholar
(11)Pati, T.On the absolute summability of Fourier series by Nörlund means. Math. Z. 88 (1965), 244–249.CrossRefGoogle Scholar
(12)Pati, T. and Dikshit, H. P.On the absolute Nörlund summability of a Fourier series at a point. To appear in Journal of Mathematics.Google Scholar
(13)Varshney, O. P.On the absolute Nörlund summability of a Fourier series. Math. Z. 83 (1964), 18–24.CrossRefGoogle Scholar