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 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.

scholarly journals On the absolute summability of Fourier series

1938 ◽  
Vol 44 (10) ◽  
pp. 733-737
Author(s):  
W. C. Randels
Keyword(s):  
Fourier Series ◽  
Absolute Summability ◽  
The Absolute ◽  
Summability Of Fourier Series

scholarly journals On approximation of signals in the generalized Zygmund class via (E, 1) (N̅, pn) summability means of conjugate Fourier series

2019 ◽  
Vol 38 (5) ◽  
pp. 981-998 ◽  
Author(s):  
T. Pradhan ◽  
S. K. Paikray ◽  
A. A. Das ◽  
Hemen Dutta
Keyword(s):  
Fourier Series ◽  
Zygmund Class ◽  
Conjugate Fourier Series ◽  
Approximation Of Signals

DEPENDENCE OF THE QUALITY OF MACHINE TRANSLATION OF THE TEXT ON THE USED FOURIER TRANSFORMATION

2021 ◽  
Vol 4 ◽  
pp. 69-80
Author(s):  
Valentin Sobchuk ◽  
◽  
Galina Kharkevych ◽  
Keyword(s):  
Fourier Series ◽  
Rate Of Convergence ◽  
Machine Translation ◽  
Fourier Transformation ◽  
Scientific Information ◽  
Necessary Condition ◽  
Linear Matrix ◽  
Matrix Methods ◽  
Filtering Algorithms ◽  
Fourier Filtering

Machine translation is widely used in the translation of commercial, technical, scientific information that is connected with the process of globalization and, accordingly, the expansion of the network of business relations. Mathematical methods related to machine translation of the texts have recently received new development due to the intensive development of Fourier transformation theory. Thus, the requirements for filtering accuracy in the processing of contrast signals and images have increased, allowing to create efficient filtering algorithms. Frequency algorithms are the most efficient of all the existing filtering algorithms, i.e., those where the coefficients of decomposition of the noisy signal by Fourier basis are the subject to processing. When using Fourier filtering algorithms, the properties of Fourier transformation play an important role, that depend on belonging to a particular class of differential functions. The necessary condition for the existence of the continuous Fourier transformation is the absolute convergence of some functions by means of which the real studied process is describing. In practice, the so-called “summation functions” are often used as simulated functions, which can be constructed using a linear matrix summation of Fourier series. As for the latter, scientists distinguish between both triangular and rectangular linear matrix methods. This paper is devoted to the study of the convergence conditions of Fourier transformations of both triangular and rectangular linear matrix methods for summing Fourier series. Moreover, this article shows that the rate of convergence of Fourier transformation of the rectangular linear Abel-Poisson method is at times faster than the rate of convergence of the analogous triangular linear Abel-Poisson method. This result can further significantly influence the choice of the more effective Fourier transformation used in the process of machine translation of the text.

On the Strong Summability by Triangular Means of the Derived Fourier Series and its Conjugate Series

1966 ◽  
Vol 9 (05) ◽  
pp. 647-654
Author(s):  
Narendra K. Govil
Keyword(s):  
Fourier Series ◽  
Triangular Matrix ◽  
Regular Sequence ◽  
Strong Summability ◽  
List Type ◽  
Conjugate Series

The triangular matrix (A) = (X ), where n = 0, 1, 2,…; k = 0, 1, 2, …; and λn, k = 0 for k > n is regular (in the sense of defining a regular sequence to sequence transform) if for every fixed k ; independently of n;

scholarly journals Random Fourier Series and Absolute Summability

1998 ◽  
Vol 28 (2) ◽  
pp. 749-765
Author(s):  
Nasser Towghi
Keyword(s):  
Fourier Series ◽  
Absolute Summability ◽  
Random Fourier Series
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