New effects of an old Z. Zalcwasser's theorem

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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 {vn}, first, Z. Zalcwasser gave an interesting condition implying the strong (C, 1)-summability of these partial sums svn (x). We show that Zalcwasser's condition on {vn} holds if and only if the subsequence {v2n} is quasi geometrically increasing. Utilizing this fact and known theorems several strong summability results are presented for given index-sequences {vn}.

Original languageEnglish
Pages (from-to)141-154
Number of pages14
JournalActa Mathematica Hungarica
Volume81
Issue number1-2
Publication statusPublished - Oct 1998

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Summability
Theorem
Orthogonal Series
Partial Sums
Subsequence
If and only if
Imply

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

New effects of an old Z. Zalcwasser's theorem. / Leindler, L.

In: Acta Mathematica Hungarica, Vol. 81, No. 1-2, 10.1998, p. 141-154.

Research output: Contribution to journalArticle

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