de la Vallée Poussin Means of Walsh-Fourier Expansions
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866909018127073280 |
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| author | Goginava, Ushangi |
| author_facet | Goginava, Ushangi |
| contents | We study de la Vallée Poussin means of Walsh--Fourier series associated with a nondecreasing window sequence. We establish a sharp criterion for almost everywhere convergence for integrable functions. We further show that, when this criterion fails, every Orlicz class below the logarithmic square-root scale contains a function whose de la Vallée Poussin means diverge everywhere. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_05135 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | de la Vallée Poussin Means of Walsh-Fourier Expansions Goginava, Ushangi Classical Analysis and ODEs We study de la Vallée Poussin means of Walsh--Fourier series associated with a nondecreasing window sequence. We establish a sharp criterion for almost everywhere convergence for integrable functions. We further show that, when this criterion fails, every Orlicz class below the logarithmic square-root scale contains a function whose de la Vallée Poussin means diverge everywhere. |
| title | de la Vallée Poussin Means of Walsh-Fourier Expansions |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2605.05135 |