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Direct Theorems on Methods of Summability

Published online by Cambridge University Press:  20 November 2018

G. G. Lorentz
G. G. Lorentz*
Affiliation:
University of Toronto
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1.1. A regular Toeplitz method of summability is given by a transformation m = 0, 1, 2 , … of the sequence sn into the sequence σm. According to the definition of regularity, every such method sums a convergent sequence sn to the value lim sn. The question naturally arises, whether there are more extensive classes of sequences summable by all regular methods 1.1(1) or at least by all such methods subject to some simple additional conditions. Questions of this kind have been treated by the author (Lorentz [2], [5]) and, from another point of view, by R. P. Agnew [2] [3] ; in this paper we wish to discuss the problem systematically.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 1 , Issue 4 , 01 August 1949 , pp. 305 - 319
Copyright
Copyright © Canadian Mathematical Society 1949

References

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