Absolute summability of orthogonal series by Euler’s method

1977 ◽  
Vol 21 (1) ◽  
pp. 29-32
Author(s):  
V. N. Spevakov ◽  
A. B. Kudryavtsev
Keyword(s):  
Orthogonal Series ◽  
Absolute Summability ◽  
Euler’S Method

On the Absolute Summability of Series with Respect to Block-Orthonormal Systems

1999 ◽  
Vol 6 (1) ◽  
pp. 83-90
Author(s):  
G. Nadibaidze
Keyword(s):  
Orthogonal Series ◽  
Absolute Summability ◽  
Almost Everywhere ◽  
Weyl Multiplier ◽  
The Absolute

Abstract Theorems determining Weyl's multipliers for the summability almost everywhere by the |c, 1| method of the series with respect to block-orthonormal systems are proved. In particular, it is stated that if the sequence {ω(n)} is the Weyl multiplier for the summability almost everywhere by the |c, 1| method of all orthogonal series, then there exists a sequence {Nk } such that {ω(n)} will be the Weyl multiplier for the summability almost everywhere by the |c, 1| method of all series with respect to the Δ k -orthonormal systems.

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.

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