Examples for the Theory of Infinite Iteration of Summability Methods

Source abstract

Garten and Knopp [ 7 ] introduced the notion of infinite iteration of Césaro (C 1 ) averages, which they called H ∞ summability. Flehinger [ 6 ] (apparently unaware of [ 7 ]) produced the first nontrivial example of an H ∞ summable sequence: the sequence ﹛a i ﹜ ∞ 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.