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Notes on Fourier series (V): Summability (R1)

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
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Extract

1·1. There is a familiar method of summation of series usually called the method (R, 1), or sometimes Lebesgue's method. 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. The method is not 'regular'; there are convergent series not summable (R, 1).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 45 , Issue 2 , April 1949 , pp. 173 - 185
Copyright
Copyright © Cambridge Philosophical Society 1949

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References

REFERENCES

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