Note on the theory of series (XXIII): On the partial sums of Fourier series
Published online by Cambridge University Press: 24 October 2008
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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