Strong summability of two-dimensional Vilenkin – Fourier series
We study the exponential uniform strong summability of two-dimensional Vilenkin – Fourier series. In particular, it is proved that the two-dimensional Vilenkin – Fourier series of a continuous function $f$ is uniformly strongly summable to a function $f$ exponentially in the power 1/2. Moreover, it...
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| Date: | 2019 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2019
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/1443 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | We study the exponential uniform strong summability of two-dimensional Vilenkin – Fourier series. In particular, it is
proved that the two-dimensional Vilenkin – Fourier series of a continuous function $f$ is uniformly strongly summable to a
function $f$ exponentially in the power 1/2. Moreover, it is proved that this result is best possible. |
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