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

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.

2021 ◽  
pp. 69
Author(s):  
N.T. Polovina

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.


2021 ◽  
pp. 54
Author(s):  
N.I. Volkova ◽  
N.S. Novikova

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.


1935 ◽  
Vol 25 ◽  
pp. 162-189 ◽  
Author(s):  
G. Hardy ◽  
J. Littlewood

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