Geodesic
A General Tauberian Condition that Implies Euler Summability
Canadian mathematical bulletin, Tome 37 (1994) no. 3, pp. 393-398

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DOI

Let V be any summability method (whether linear or conservative or not), 0 < p < 1 and s a real or complex sequence. Let Ep denote the matrix of the Euler method. A theorem is proved, giving a condition under which the V-summability of Eps will imply the Ep -summability of s. This extends, in generalized form, an earlier result of N. H. Bingham who considered the case where s is a real sequence and V = B (Borel's method). It is also proved that even for real sequences, the condition given in the theorem cannot be replaced by the condition used by Bingham.
DOI : 10.4153/CMB-1994-057-5
Mots-clés : Primary: 40G05, secondary: 40E99 
Parameswaran, Mangalam R. A General Tauberian Condition that Implies Euler Summability. Canadian mathematical bulletin, Tome 37 (1994) no. 3, pp. 393-398. doi: 10.4153/CMB-1994-057-5
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     title = {A {General} {Tauberian} {Condition} that {Implies} {Euler} {Summability}},
     journal = {Canadian mathematical bulletin},
     pages = {393--398},
     year = {1994},
     volume = {37},
     number = {3},
     doi = {10.4153/CMB-1994-057-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1994-057-5/}
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