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On the absolute summability and convergence of Fourier series and associated series

Published online by Cambridge University Press:  24 October 2008

M. K. Nayak
M. K. Nayak
Affiliation:
Panjab University, Chandigarh—14, India
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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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References

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