The (l)-property of the semicontinuous logarithmic method of summation of series and Tauberian theorems

1975 ◽  
Vol 26 (5) ◽  
pp. 493-499
Author(s):  
A. P. Kokhanovskii
Keyword(s):  
Tauberian Theorems ◽  
Logarithmic Method ◽  
Summation Of Series

Some Tauberian Theorems for the Logarithmic Method of Summability

1968 ◽  
Vol 20 ◽  
pp. 1324-1331 ◽  
Author(s):  
B. Kwee
Keyword(s):  
Tauberian Theorems ◽  
Logarithmic Method ◽  
Image Position

The series is said to be summable (L) to s if the sequence {sn}, where sn = a0 + a1 + … + an, is L-convergent to s, i.e., ifIf the sequence {sn} is l-convergent to s, i.e., if the sequence {tn}, where1

Tauberian Theorems for Integrals

1963 ◽  
Vol 15 ◽  
pp. 433-439
Author(s):  
Ralph Henstock
Keyword(s):  
Theorem Proving ◽  
Tauberian Theorems ◽  
Cesàro Means ◽  
Cesàro Mean ◽  
B Method ◽  
Summation Of Series ◽  
Cesáro Means ◽  
Abelian Theorem ◽  
Cesaro Mean ◽  
Abel Mean

When, for the generalized summation of series, we use A and B methods, giving A and B sums, respectively, we say that the A method is included in the B method, A ⊂ B, if the B sum exists and is equal to the A sum whenever the latter exists. A theorem proving such a result is called an Abelian theorem. For example, there is an Abelian theorem stating that if the A and B sums are the first Cesàro mean and the Abel mean, respectively, then A ⊂ B. If A ⊂ B and B ⊂ A, we say that A and B are equivalent, A = B. For example, the nth Hölder and nth. Cesàro means are equivalent.

A property of a class of (�R, Pn,?) methods for summation of series and Tauberian theorems

1977 ◽  
Vol 29 (2) ◽  
pp. 145-152 ◽  
Author(s):  
G. A. Mikhalin ◽  
L. S. Teslenko
Keyword(s):  
Tauberian Theorems ◽  
Summation Of Series

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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