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Examples for the Theory of Infinite Iteration of Summability Methods

Published online by Cambridge University Press:  20 November 2018

Persi Diaconis
Persi Diaconis*
Affiliation:
Stanford University, Stanford, California
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Abstract

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Garten and Knopp [7] introduced the notion of infinite iteration of Césaro (C1 ) averages, which they called H∞ summability. Flehinger [6] (apparently unaware of [7]) produced the first nontrivial example of an H∞ summable sequence: the sequence ﹛ai ﹜ ∞i=1 where at is 1 or 0 as the lead digit of the integer i is one or not. Duran [2] has provided an elegant treatment of H∞ summability as a special case of summability with respect to an ergodic semigroup of transformations.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 3 , 01 June 1977 , pp. 489 - 497
Copyright
Copyright © Canadian Mathematical Society 1977

References

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