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

1976 ◽  
Vol 28 (1) ◽  
pp. 81-85
Author(s):  
K. M. Slepenchuk
Keyword(s):  
Double Series ◽  
Absolute Summability ◽  
Matrix Methods ◽  
Tauberian Type

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 summability of power $p$ of series, associated with conjugate Fourier series, by triangular matrix methods

2021 ◽  
pp. 54
Author(s):  
N.I. Volkova ◽  
N.S. Novikova
Keyword(s):  
Fourier Series ◽  
Triangular Matrix ◽  
Absolute Summability ◽  
Matrix Methods ◽  
Conjugate Fourier Series

We establish conditions of absolute summability of powers of series that are associated with conjugate Fourier series, by triangular matrix methods, and provide the application of the theorems proved to Voronoi-Nerlund method.

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.

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.

Tauberian type theorems for double series summable by Cesaro methods

1972 ◽  
Vol 23 (6) ◽  
pp. 597-606 ◽  
Author(s):  
M. A. Kalatalova
Keyword(s):  
Double Series ◽  
Tauberian Type

Theorems of Tauberian type for matrix transformations of double series

1991 ◽  
Vol 43 (5) ◽  
pp. 662-667
Author(s):  
K. M. Slepenchuk
Keyword(s):  
Double Series ◽  
Matrix Transformations ◽  
Tauberian Type

Invertibility conditions in the theory of absolute summability of double series

1980 ◽  
Vol 32 (2) ◽  
pp. 107-111 ◽  
Author(s):  
K. M. Slepenchuk
Keyword(s):  
Double Series ◽  
Absolute Summability

Conditions for the absolute summability in power p of double series

1990 ◽  
Vol 48 (5) ◽  
pp. 589-593
Author(s):  
K. M. Slepenchuk
Keyword(s):  
Double Series ◽  
Absolute Summability ◽  
The Absolute

scholarly journals Summability of Orthogonal Series by Absolute Matrix Method: قابلية جمع المتسلسلات المتعامدة بالطريقة المصفوفية المطلقة

2020 ◽  
Vol 4 (3) ◽  
Author(s):  
Ghina Mohammed Gehad Alhashemi, Mohammed Mahmoud Amer
Keyword(s):  
Matrix Method ◽  
Orthogonal Series ◽  
Natural Generalization ◽  
Absolute Summability ◽  
Research Articles ◽  
Orthogonal Functions ◽  
Matrix Methods ◽  
Summability Methods ◽  
Special Cases

At the beginning of the 20th century, the theory of perpendicular series orthogonal, which treated sentences of orthogonal functions as a natural generalization of series theory. The perpendicular mass idyllability many methods, such as the Reimann, Norlund, Cesaro, Holder, and generalized Norlund methods, has been studied. In this research, we studied the summability of simple orthogonal series in different methods called absolute methods that rely heavily on differences. This is done by relying on some research, articles and scientific books in the field of summability of series. The absolute matrix methods are one of the most important methods of absolute summability. Most absolute summability methods are special cases of absolute matrix method. We finally recommend a double case study.

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
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