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Notes on the theory of series (III): On the summability of the Fourier series of a nearly continuous function

Published online by Cambridge University Press:  24 October 2008

G. H. Hardy  and
J. E. Littlewood
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Extract

The theorem which we prove here seems obvious enough when stated, but it appears to have been overlooked by the numerous writers who have discussed the subject, and the proof is less immediate than might be expected.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 23 , Issue 6 , April 1927 , pp. 681 - 684
Copyright
Copyright © Cambridge Philosophical Society 1927

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References

1.Chapman, S.. ‘On non-integral orders of summability of series and integrals’, Proc. London Math. Soc. (2), 9 (1910), 369–409.Google Scholar
2.Hardy, G. H., ‘On the suminability of Fourier series’, Proc. London Math. Soc. (2), 12 (1913), 365–372.CrossRefGoogle Scholar
3.Hobson, E. W., The theory of functions of a real variable, 2 (ed. 2, 1926), 567.Google Scholar
4.Riesz, M., ‘Sur les séries de Dirichlet et les séries entières’, Comptes rendus, 22 11. 1909.Google Scholar
5.Riesz, M., ‘Sur la sommation des séries de Fourier’, Acta Reg. Univ. Francuco-Josephinae (Szeged), 1 (1923), 104–113.Google Scholar
6.Young, W. H., ‘Über eine Summationsmethode für die Fouriersche Reihe’, Leipziger Berichte, 63 (1911), 369–387.Google Scholar
7.Young, W. H., ‘On infinite integrals involving a generalisation of the sine and cosine functions’, Quarterly Journal, 43 (1912), 161–177.Google Scholar
8.Young, W. H., ‘On the convergence of a Fourier series and of its allied series’, Proc. London Math. Soc. (2), 10 (1912), 254–272.CrossRefGoogle Scholar