Notes on the Theory of Series (XVIII): on the Convergence of Fourier Series
Published online by Cambridge University Press: 24 October 2008
Extract
1. In this note we give first our proof of a theorem (Theorem 1) which we stated in Note XIII. We then prove a new theorem (Theorem 2) which leads to another proof of the main theorem of Note XVII.
The first of these theorems requires some preliminary explanations. We are concerned with an integrable function f (θ) with the period 2π. We write
being the complex Fourier series of f (θ).
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 31 , Issue 3 , July 1935 , pp. 317 - 323
- Copyright
- Copyright © Cambridge Philosophical Society 1935
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