On products of summability methods
β Scribed by M. S. Ramanujan
- Publisher
- Springer-Verlag
- Year
- 1958
- Tongue
- French
- Weight
- 303 KB
- Volume
- 69
- Category
- Article
- ISSN
- 0025-5874
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π SIMILAR VOLUMES
In this paper we consider generalized Norlund methods (Nap), a > -1, power series methods (J,) and the iteration product of two such methods. A particular case is that of the Cesaro means (C,) with corresponding power series method (A), i.e., Abel's method. We obtain generalizations of inclusion, an
Let T = (tm,J (m, n = I, 2 ,...; all t,,, , > 0) define a regular summability method. It is known [l] that there is a bounded divergent sequence whose T-transform is also divergent. Here we point out that one can say more: namely, that for some real, bounded, divergent sequence {a,}~=, , its T-trans