Determination of jumps in terms of linear operators
A theorem of Luk´acs [4] states that the partial sums of conjugate Fourier series of a periodic Lebesgue integrable function $f$ diverge with a logarithmic rate at the points of discontinuity of $f$ of the first kind. M´oricz [5] proved a similar theorem for the rectangular partial sums of double va...
Збережено в:
| Дата: | 2015 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2015
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/2097 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | A theorem of Luk´acs [4] states that the partial sums of conjugate Fourier series of a periodic Lebesgue integrable function $f$ diverge with a logarithmic rate at the points of discontinuity of $f$ of the first kind. M´oricz [5] proved a similar theorem for the rectangular partial sums of double variable functions.
We consider analogs of the M´oricz theorem for generalized Ces´aro means and for positive linear means.
We consider a similar theorem in terms of linear operators satisfying certain conditions. |
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