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 | Zendy

N.T. Polovina | Zendy

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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

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.

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