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On Hausdorff's methods of summability. II

Published online by Cambridge University Press:  24 October 2008

W. W. Rogosinski
W. W. Rogosinski
Affiliation:
King's CollegeAberdeen
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Extract

A general theory of ‘strength’ for Hausdorff methods T of summability was given in the first part of this paper, to which we shall refer in the following as I. Those methods T which are regular (that is, at least as strong as ordinary convergence C), are defined by the linear transforms

of a given sequence (sk). Here ø(t) (that is, each of its real and imaginary parts) is of bounded variation (b.v.) in the closed interval 〈0, 1〉 [see I, (4)]. The additional condition for consistency (with C) is that ø(t) is continuous at t = 0, and that ø(1) − ø(0) = 1 [I, H. 3]. We write also T ˜ ø(t).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 38 , Issue 4 , November 1942 , pp. 344 - 363
Copyright
Copyright © Cambridge Philosophical Society 1942

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References

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