Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-29T18:59:26.534Z Has data issue: false hasContentIssue false
  • English
  • Français

Notes on Fourier series (IV): Summability (R2)

Published online by Cambridge University Press:  24 October 2008

G. H. Hardy  and
W. W. Rogosinski
G. H. Hardy
Affiliation:
Trinity CollegeCambridge
W. W. Rogosinski
Affiliation:
King's CollegeNewcastle on Tyne
Get access Rights & Permissions [Opens in a new window]

Extract

1.1. There are two familiar methods of summation of divergent series usually called the methods (R, 1) and (R, 2). If sn = u0 + u1 + … + un and, as it will be convenient to suppose throughout, u0 = 0, then

when h → + 0§: the convergence of the series for small positive h is presupposed.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 43 , Issue 1 , January 1947 , pp. 10 - 25
Copyright
Copyright © Cambridge Philosophical Society 1947

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Hardy, G. H. and Littlewood, J. E.Math. Z. 19 (1923), 67–96.CrossRefGoogle Scholar
(2)Hardy, G. H., Littlewood, J. E. and Pólya, G.Inequalities (Cambridge, 1934).Google Scholar
(3)Hardy, G. H. and Rogosinski, W. W.Fourier series (Cambridge, 1944).Google Scholar
(4)Kuttner, B.Proc. London Math. Soc. (2), 40 (1936), 524–40.CrossRefGoogle Scholar
(5)Marcinkiewicz, J.J. London Math. Soc. 10 (1935), 268–72.CrossRefGoogle Scholar
(6)Titchmarsh, E. C.Introduction to the theory of Fourier integrals (Oxford, 1937).Google Scholar
(7)Wang, F. T.Tôhoku Math. J. 41 (1935), 91–108.Google Scholar
(8)Wiener, N.Amer. J. Math. 45 (1923), 83–6.CrossRefGoogle Scholar
(9)Zygmund, A.Trigonometrical series (Warsaw, 1935).Google Scholar