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On the limits of oscillation of a function and its Cesàro means

Published online by Cambridge University Press:  20 January 2009

C. T. Rajagopal
C. T. Rajagopal
Affiliation:
Madras Christian College, Tambaram, Madras, S. India.
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There is a group of Tauberian theorems of which the simplest isone due to K. Ananda Rau [Theorem 2 of the paper numbered 1 inthe list of references at the end of the note]. More complicatedtheorems of the same group are discussed in a paper by S.Minakshisundaram and myself to be published by the LondonMathematical Society [4].

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 7 , Issue 3 , February 1946 , pp. 162 - 167
Copyright
Copyright © Edinburgh Mathematical Society 1946

References

REFERENCES

1.Bosanquet, L. S., “Note on convexity theorems,” Journal London Math. Soc., 18 (1943), 239–248.CrossRefGoogle Scholar
2.Karamata, J., “Beziehungen zwischen den Oscillationsgrenzen einer Funktion und ihrer arithmetischen Mittel,” Proc. London Math. Soc.,. (2) 43 (1937), 20–25.Google Scholar
3.Minakshisundaram, S., “A Tauberian theorem on (λ k) — process of summation,” Journal Indian Math. Soc. (New Series), 4 (1938), 127–130.Google Scholar
4.Minakshisundaram, S. and Rajagopal, C. T., “ An extension of a Tauberian theorem of L. J. Mordell” (to be published by the London Math. Soc).Google Scholar