### 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_{vn} (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}}.

Original language | English |
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Pages (from-to) | 141-154 |

Number of pages | 14 |

Journal | Acta Mathematica Hungarica |

Volume | 81 |

Issue number | 1-2 |

Publication status | Published - Oct 1998 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Acta Mathematica Hungarica*,

*81*(1-2), 141-154.

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

Research output: Contribution to journal › Article

*Acta Mathematica Hungarica*, vol. 81, no. 1-2, pp. 141-154.

}

TY - JOUR

T1 - New effects of an old Z. Zalcwasser's theorem

AU - Leindler, L.

PY - 1998/10

Y1 - 1998/10

N2 - 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}.

AB - 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}.

UR - http://www.scopus.com/inward/record.url?scp=0032221385&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032221385&partnerID=8YFLogxK

M3 - Article

VL - 81

SP - 141

EP - 154

JO - Acta Mathematica Hungarica

JF - Acta Mathematica Hungarica

SN - 0236-5294

IS - 1-2

ER -