On the absolute summability and convergence of Fourier series and associated series
Published online by Cambridge University Press: 24 October 2008
Extract
1. We suppose that f(t) is integrable L and periodic with period 2π and we denote the Fourier series of f(t) at the point t = x by
We denote the nth partial sum of the Fourier series by sn. We will prove here a general result (i.e Theorem 1) and some interesting results in connexion with associated series of a Fourier series of the type
We write
The object of the present paper is to prove the following theorems. (In all the following cases k is any constant > π if nothing else is mentioned.)
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 70 , Issue 3 , November 1971 , pp. 421 - 433
- Copyright
- Copyright © Cambridge Philosophical Society 1971
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