Approximation by Abel means and Tauberian Theorems in sequences spaces

1982 ◽  
Vol 74 (2) ◽  
pp. 123-136
Author(s):  
Martin Buntinas
Keyword(s):  
Tauberian Theorems ◽  
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.

Classical Tauberian Theorems for the (C; 1; 1) Summability Method

2014 ◽  
Vol 0 (0) ◽  
Author(s):  
Ümit Totur
Keyword(s):  
Tauberian Theorem ◽  
Summability Method ◽  
Subject Classification ◽  
Tauberian Theorems ◽  
Double Sequences ◽  
Littlewood Theorem

Abstract In this paper we generalize some classical Tauberian theorems for single sequences to double sequences. One-sided Tauberian theorem and generalized Littlewood theorem for (C; 1; 1) summability method are given as corollaries of the main results. Mathematics Subject Classification 2010: 40E05, 40G0

Tauberian Theorems for Sequences linked by a Convolution

1998 ◽  
Vol 193 (1) ◽  
pp. 211-234 ◽  
Author(s):  
Richard Warlimont
Keyword(s):  
Tauberian Theorems

scholarly journals One-Sided Tauberian Theorems for Dirichlet Series Methods of Summability

2001 ◽  
Vol 31 (3) ◽  
pp. 797-830 ◽  
Author(s):  
David Borwein ◽  
Werner Kratz ◽  
Ulrich Stadtmüller
Keyword(s):  
Dirichlet Series ◽  
Tauberian Theorems

Tauberian theorems in a Banach lattice, with applications to the LP spaces

1954 ◽  
Vol 50 (2) ◽  
pp. 242-249
Author(s):  
D. C. J. Burgess
Keyword(s):  
Banach Space ◽  
Banach Lattice ◽  
Laplace Transforms ◽  
Tauberian Theorems ◽  
General Argument ◽  
Arbitrary Banach Space ◽  
Lp Spaces ◽  
Special Case

In a previous paper (2) of the author, there was given a treatment of Tauberian theorems for Laplace transforms with values in an arbitrary Banach space. Now, in § 2 of the present paper, this kind of technique is applied to the more special case of Laplace transforms with values in a Banach lattice, and investigations are made on what additional results can be obtained by taking into account the existence of an ordering relation in the space. The general argument is again based on Widder (5) to which frequent references are made.

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