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On the Nörlund summability of Fourier series

Published online by Cambridge University Press:  24 October 2008

C. T. Rajagopal
C. T. Rajagopal
Affiliation:
Ramanujan Institute of Mathematics, University of Madras
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Extract

1. The purpose of this note is to prove a result which includes certain classical theorems generally thought of as being unconnected; in explicit terms, a result about the Fourier series of a periodic Lebesgue-integrable function showing that the series is summable at a point by a Nörlund method (N, pn) defined as usual ((2), p. 64) if pn ↓ 0, Σpn = ∞ and the point is in a certain subset of the Lebesgue set. More precisely, the purpose is to prove Theorem I on the Nörlund summability of Fourier series and to derive from it the well-known Theorems A, B which follow and the recent extension of Theorem A in Theorem A' which appears later and is due to Sahney (8).

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 59 , Issue 1 , January 1963 , pp. 47 - 53
Copyright
Copyright © Cambridge Philosophical Society 1963

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References

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