Strong summability of double series by matrix methods and Tauberian theorems for these methods

1975 ◽  
Vol 17 (3) ◽  
pp. 227-232
Author(s):  
K. M. Slepenchuk
Keyword(s):  
Double Series ◽  
Strong Summability ◽  
Tauberian Theorems ◽  
Matrix Methods

scholarly journals Tauberian theorems in the case of strong summability in degree $p$ of double series

2021 ◽  
pp. 84
Author(s):  
T.N. Yarkovaia
Keyword(s):  
Tauberian Theorem ◽  
Double Series ◽  
Strong Summability ◽  
Tauberian Theorems ◽  
Matrix Methods

We establish a Tauberian theorem in the case of strong summability in degree $p$ of double series by matrix methods, give its application to Abel methods.

scholarly journals Tauberian theorems in the case of absolute summability in degree $p$ of double series

2021 ◽  
pp. 90
Author(s):  
T.N. Yarkovaia
Keyword(s):  
Tauberian Theorem ◽  
Double Series ◽  
Absolute Summability ◽  
Tauberian Theorems ◽  
Matrix Methods

We establish a Tauberian theorem in the case of absolute summability in degree $p$ of double series by matrix methods, give its application to Abel methods.

scholarly journals Absolute and strong summability in degree $p \geqslant 1$ of $r$ times differentiated Fourier series and $r$ times differentiated conjugate Fourier series by matrix methods

2021 ◽  
pp. 74
Author(s):  
N.T. Polovina
Keyword(s):  
Fourier Series ◽  
Strong Summability ◽  
Matrix Methods ◽  
Conjugate Fourier Series ◽  
The Matrix

We establish conditions of $|\gamma|_p$- and $[\gamma]_p$-summability in degree $p \geqslant 1$ of $r$ times differentiated Fourier series at the point where $\gamma = \| \gamma_{nk} \|$ is the matrix of transformation of series to sequence. Analogous conditions are considered also for $r$ times differentiated conjugate Fourier series.

Absolute Summability Factors and Absolute Tauberian Theorems for Double Series and Sequences

1999 ◽  
Vol 6 (6) ◽  
pp. 591-600
Author(s):  
Sh. Yanetz (Chachanashvili)
Keyword(s):  
Double Series ◽  
Absolute Summability ◽  
Tauberian Theorems ◽  
Summability Factors ◽  
Tauberian Conditions ◽  
Absolute Summability Factors

Abstract Let 𝐴 and 𝐵 be the linear methods of the summability of double series with fields of bounded summability and , respectively. Let 𝑇 be certain set of double series. The condition 𝑥 ∈ 𝑇 is called 𝐵𝑏-Tauberian for 𝐴 if . Some theorems about summability factors enable one to find new 𝐵𝑏-Tauberian conditions for 𝐴 from the already known 𝐵𝑏-Tauberian conditions for 𝐴.

scholarly journals A bounded consistency theorem for strong summabilities

1989 ◽  
Vol 12 (1) ◽  
pp. 39-46 ◽  
Author(s):  
C. S. Chun ◽  
A. R. Freedman
Keyword(s):  
Strong Summability ◽  
Regular Matrix ◽  
Matrix Methods ◽  
Summability Methods ◽  
Summability Field

The study of R-type summability methods is continued in this paper by showing that two such methods are identical on the bounded portion of the strong summability field associated with the methods. It is shown that this “bounded consistency” applies for many non-matrix methods as well as for regular matrix methods.

scholarly journals Gap Tauberian theorems

1993 ◽  
Vol 47 (3) ◽  
pp. 385-393 ◽  
Author(s):  
Jeff Connor
Keyword(s):  
Tauberian Theorem ◽  
Strong Summability ◽  
Tauberian Theorems ◽  
Weighted Mean ◽  
Tauberian Condition ◽  
Support Set ◽  
Tauberian Conditions ◽  
Summability Matrix ◽  
Regular Summability ◽  
Bk Spaces

In the first section we establish a connection between gap Tauberian conditions and isomorphic copies of Co for perfect coregular conservative BK spaces and in the second we give a characterisation of gap Tauberian conditions for strong summability with respect to a nonnnegative regular summability matrix. These results are used to show that a gap Tauberian condition for strong weighted mean summability is also a gap Tauberian condition for ordinary weighted mean summability. We also make a remark regarding the support set of a matrix and give a Tauberian theorem for a class of conull spaces.

scholarly journals Absolute and strong summability in degree $p \geqslant 1$ of series, associated with Fourier series, by matrix methods

2021 ◽  
pp. 69
Author(s):  
N.T. Polovina
Keyword(s):  
Fourier Series ◽  
Strong Summability ◽  
Matrix Methods ◽  
The Matrix

We establish conditions of $|\gamma|_p$- and $[\gamma]_p$-summability in degree $p \geqslant 1$ of series, associated with Fourier series, at the point where $\gamma = \| \gamma_{nk} \|$ is the matrix of transformation of series to sequence.

On Tauberian Theorems for Double Series

1940 ◽  
Vol 62 (1/4) ◽  
pp. 666 ◽  
Author(s):  
Ralph Palmer Agnew
Keyword(s):  
Double Series ◽  
Tauberian Theorems

scholarly journals On conditions of strong, of degree $p$, summability of number series

1987 ◽  
pp. 99
Author(s):  
N.T. Polovina ◽  
K.M. Slepenchuk
Keyword(s):  
Double Series ◽  
Strong Summability ◽  
Number Series

We establish the conditions of $[\Gamma]_p$-summability of number series, more convenient for applications. Besides, we establish the conditions of $[A]$-summability of number series and give applications of proved theorems in case of strong summability of double series.

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