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New Effects of an Old Z. Zalcwasser's Theorem
Authors:L Leindler
Institution:1. Bolyai Intézet Aradi Vértanúk Tere 1 Szeged, Hungary, H-6720
Abstract:It is well known that the strong (C, 1)-summability of an orthogonal series does not imply its very strong (C, 1)-summability, generally. For a given index-sequence {v n }, first, Z. Zalcwasser gave an interesting condition implying the strong (C, 1)-summability of these partial sums s v n (x). We show that Zalcwasser's condition on {v n } holds if and only if the subsequence {v 2 n} is quasi geometrically increasing. Utilizing this fact and known theorems several strong summability results are presented for given index-sequences {v n }.
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