DISCRETE ABEL MEANS

Analysis ◽  
1990 ◽  
Vol 10 (2-3) ◽  
Author(s):  
David H. Armitage ◽  
Ivor J. Maddox
Keyword(s):  
Abel Means

Abel means of operator-valued processes

1995 ◽  
Vol 115 (3) ◽  
pp. 261-276 ◽  
Author(s):  
G. Blower
Keyword(s):  
Abel Means

scholarly journals GROWTH ORDERS OF CESÀRO AND ABEL MEANS OF FUNCTIONS IN BANACH SPACES

2010 ◽  
Vol 14 (3B) ◽  
pp. 1201-1248
Author(s):  
Jeng-Chung Chen ◽  
Ryotaro Sato ◽  
Sen-Yen Shaw
Keyword(s):  
Banach Spaces ◽  
Abel Means

Abel extensions of some classical Tauberian theorems

2019 ◽  
Vol 28 (2) ◽  
pp. 105-112
Author(s):  
ERDAL GUL ◽  
MEHMET ALBAYRAK
Keyword(s):  
Tauberian Theorem ◽  
Matrix Method ◽  
Tauberian Theorems ◽  
Borel Summability ◽  
Tauberian Condition ◽  
Continuous Parameter ◽  
Abel Means ◽  
The One ◽  
Abel Mean

The well-known classical Tauberian theorems given for Aλ (the discrete Abel mean) by Armitage and Maddox in [Armitage, H. D and Maddox, J. I., Discrete Abel means, Analysis, 10 (1990), 177–186] is generalized. Similarly the ”one-sided” Tauberian theorems of Landau and Schmidt for the Abel method are extended by replacing lim As with Abel-lim Aσi n(s). Slowly oscillating of {sn} is a Tauberian condition of the Hardy-Littlewood Tauberian theorem for Borel summability which is also given by replacing limt(Bs)t = `, where t is a continuous parameter, with limn(Bs)n = `, and further replacing it by Abel-lim(Bσi k (s))n = `, where B is the Borel matrix method.

scholarly journals Equivalence results for discrete Abel means

2002 ◽  
Vol 30 (12) ◽  
pp. 727-731
Author(s):  
Jeffrey A. Osikiewicz
Keyword(s):  
Summability Method ◽  
Abel Summability ◽  
Abel Means ◽  
Abel Mean ◽  
Bounded Sequences

We present theorems showing when the discrete Abel mean and the Abel summability method are equivalent for bounded sequences and when two discrete Abel means are equivalent for bounded sequences.

scholarly journals A Theorem on General Regular Transformations of Series

1956 ◽  
Vol 9 (3) ◽  
pp. 105-108
Author(s):  
Arwel Evans
Keyword(s):  
Infinite Number ◽  
Linear Form ◽  
Linear Transformations ◽  
Non Linear ◽  
Abel Means ◽  
Image Position ◽  
Almost All

Many papers have been written on transformations of sequences which can be written aswhere is a function of a finite or infinite number of variables for fixed m. If the number of variables is finite it becomes large with m.Almost all these papers are on linear transformations of the sr, e.g. Cesàro and Abel means, but there are obvious transformations of non-linear form which are regular, and it is a theorem on these which is considered here.

An Integral for Cesàro Summable Series

1967 ◽  
Vol 10 (1) ◽  
pp. 85-97 ◽  
Author(s):  
George Cross
Keyword(s):  
Trigonometric Series ◽  
Extra Condition ◽  
Conjugate Series ◽  
Abel Means ◽  
Image Position

The pk+2 - integral of James [2] is strong enough to integrate a trigonometric series of the form1.1which is summable (C, k) in [0,2π], provided an extra condition holds involving the conjugate series1.2Considering series with coefficients o(n), Taylor [5] constructed an integral (the AP-integral) which successfully integrates series of the form (1. 1) which are Abel summable provided an extra condition holds involving the Abel means of the conjugate series (1.2).

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