Open AccessComplete proofs of the main theorems on summability factors
Author(s) -
Simson Baron,
Alexander Peyerimhoff
Publication year - 1999
Publication title -
acta et commentationes universitatis tartuensis de mathematica./acta et commentationes universitatis tartuensis de mathematica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.276
H-Index - 6
eISSN - 2228-4699
pISSN - 1406-2283
DOI - 10.12697/acutm.1999.03.03
Subject(s) - mathematical proof , mathematics , calculus (dental) , pure mathematics , algebra over a field , discrete mathematics , geometry , medicine , dentistry
In this article the shortest proofs up to the present of the main theorems on summability factors for Cesàro methods are given. The necessity part of these theorems is proved for more general methods. Especially short is the proof of the sufficiency part of the theorem for summability factors of types (C0α,|Cβ|) and (Cα,|Cβ|).