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On Converse Theorems of Summability

Published online by Cambridge University Press:  03 November 2016

C. T. Rajagopal
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This paper, while it does not merit the attention of workers in the field of summability, may be of some interest to readers of the Gazette who are using Bromwich's classical work on infinite series as a textbook. Its main purpose is to show that Bromwich's proof of the Hardy-Landau converse of Cauchy's limit theorem can be made to yield, without any modification of the underlying idea (due to A. E. Jolliffe), all the familiar converse theorems on Rieszian summability of the first order. The paper also shows that after having obtained these theorems, one can pass on, by a natural transition suggested by Szász, to the corresponding results in the theory of summability by Dirichlet's series

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Type
Research Article
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The Mathematical Gazette , Volume 30 , Issue 292 , December 1946, pp. 272 - 276
Copyright
Copyright © Mathematical Association 1946

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References

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