Open AccessAbsolute and strong summability in degree $p \geqslant 1$ of $r$ times differentiated Fourier series and $r$ times differentiated conjugate Fourier series by matrix methods
Author(s) -
N.T. Polovina
Publication year - 2021
Publication title -
researches in mathematics
Language(s) - English
Resource type - Journals
eISSN - 2664-5009
pISSN - 2664-4991
DOI - 10.15421/247719
Subject(s) - fourier series , series (stratigraphy) , mathematics , conjugate fourier series , degree (music) , matrix (chemical analysis) , fourier transform , conjugate , sequence (biology) , fourier analysis , mathematical analysis , physics , short time fourier transform , materials science , chemistry , paleontology , biochemistry , acoustics , biology , composite material
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.