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Note on the theory of series (XXIII): On the partial sums of Fourier series

Published online by Cambridge University Press:  24 October 2008

G. H. Hardy  and
J. E. Littlewood
G. H. Hardy
Affiliation:
Trinity CollegeCambridge
J. E. Littlewood
Affiliation:
Trinity CollegeCambridge
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Extract

1. In what follows f(θ) is a periodic function of L2,

is the Fourier series of f(θ), and

is the nth partial sum of T(θ). We denote by n(θ) any function of θ which is measurable, is finite p.p. †, and assumes non-negative integral values only, and by n(θ, H) an n(θ) none of whose values exceeds H. We shall sometimes write N for n(θ), and N(H) for n(θ, H), to simplify the set-up of formulae.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 40 , Issue 2 , June 1944 , pp. 103 - 107
Copyright
Copyright © Cambridge Philosophical Society 1944

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References

REFERENCES

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